Big Ideas Math Geometry Answers Chapter 3

Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines

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Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines covers questions from Exercises, Chapter Tests, Review Tests, Assessments, Cumulative Practice, etc. Learn Math in a fun way and practice Big Ideas Math Geometry Chapter 3 Parallel and Perpendicular Lines Answers on a daily basis. Enhance your confidence levels by solving from the Parallel and Perpendicular Lines Big Ideas Math Geometry Answers Chapter 3 and attempt the exams well.

Big Ideas Math Book Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines

Learn the concepts quickly using the BIM Book Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines. For a better learning experience, we have compiled all the Big Ideas Math Geometry Answers Chapter 3 as per the Big Ideas Math Geometry Textbooks format. You can find all the concepts via the quick links available below. Simply tap on them and learn the fundamentals involved in the Parallel and Perpendicular Lines Chapter.

Parallel and Perpendicular Lines Maintaining Mathematical Proficiency

Find the slope of the line.

Question 1.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 1
Answer:

Question 2.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 2
Answer:

Question 3.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3
Answer:

Write an equation of the line that passes through the given point and has the given slope.

Question 4.
(6, 1); m = – 3
Answer:

Question 5.
(-3, 8); m = – 2
Answer:

Question 6.
(- 1, 5); m = 4
Answer:

Question 7.
(2, – 4); m = \(\frac{1}{2}\)
Answer:

Question 8.
(- 8, – 5); m = –\(\frac{1}{4}\)
Answer:

Question 9.
(0, 9); m = \(\frac{2}{3}\)
Answer:

Question 10.
ABSTRACT REASONING
Why does a horizontal line have a slope of 0, but a vertical line has an undefined slope?
Answer:

Parallel and Perpendicular Lines Mathematical Practices

Use a graphing calculator to graph the pair of lines. Use a square viewing window. Classify the lines as parallel, perpendicular, coincident, or non perpendicular intersecting lines. Justify your answer.

Question 1.
x + 2y = 2
2x – y = 4
Answer:

Question 2.
x + 2y = 2
2x + 4y = 4
Answer:

Question 3.
x + 2y = 2
x + 2y = – 2
Answer:

Question 4.
x – 2y = 2
x – y = – 4
Answer:

3.1 Pairs of Lines and Angles

Exploration 1

Points of intersection

work with a partner: Write the number of points of intersection of each pair of coplanar lines.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 4
Answer:

Exploration 2

Classifying Pairs of Lines

Work with a partner: The figure shows a right rectangular prism. All its angles are right angles. Classify each of the following pairs of lines as parallel, intersecting, coincident, or skew. Justify your answers. (Two lines are skew lines when they do not intersect and are not coplanar.)
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 5
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 6
Answer:

Exploration 3

Identifying Pairs of Angles

Work with a partner: In the figure, two parallel lines are intersected by a third line called a transversal.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 7
a. Identify all the pairs of vertical angles. Explain your reasoning.
CONSTRUCTING VIABLE ARGUMENTS
To be proficient in math, you need to understand and use stated assumptions, definitions, and previously established results.
Answer:

b. Identify all the linear pairs of angles. Explain your reasoning.
Answer:

Communicate Your Answer

Question 4.
What does it mean when two lines are parallel, intersecting, coincident, or skew?
Answer:

Question 5.
In Exploration 2. find three more pairs of lines that are different from those given. Classify the pairs of lines as parallel, intersecting, coincident, or skew. Justify your answers.
Answer:

Lesson 3.1 Pairs of Lines and Angles

Monitoring Progress

Question 1.
Look at the diagram in Example 1. Name the line(s) through point F that appear skew to Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 8.
Answer:

Question 2.
In Example 2, can you use the Perpendicular Postulate to show that Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 9 is not perpendicular to Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 10? Explain why or why not.
Answer:

Classify the pair of numbered angles.

Question 3.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 11
Answer:

Question 4.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 12
Answer:

Question 5.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 13
Answer:

Exercise 3.1 Pairs of Lines and Angles

Vocabulary and Core Concept Check

Question 1.
COMPLETE THE SENTENCE
Two lines that do not intersect and are also not parallel are ________ lines.
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 1

Question 2.
WHICH ONE DOESN’T BELONG?
Which angle pair does not belong with the other three? Explain our reasoning.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 14
∠2 and ∠3
∠4 and ∠5
∠1 and ∠8
∠2 and∠7
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3 – 6, think of each segment in the diagram as part of a line. All the angles are right angles. Which line(s) or plane(s) contain point B and appear to fit the description?
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 15
Question 3.
line(s) parallel to Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 16.
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 3

Question 4.
line(s) PerPendicular to Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 17.
Answer:

Question 5.
line(s) skew to Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 18
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 5

Question 6.
plane(s) parallel to plane CDH
Answer:

In Exercises 7-10, Use the diagram.

Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 19

Question 7.
Name a pair of parallel lines.
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 7

Question 8.
Name a pair of perpendicular lines.
Answer:

Question 9.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 20
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 9

Question 10.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 21
Answer:

In Exercises 11-14, identify all pairs of angles of the given type.

Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 22
Question 11.
corresponding
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 11

Question 12.
alternate interior
Answer:

Question 13.
alternate exterior
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 13

Question 14.
consecutive interior
Answer:

USING STRUCTURE
In Exercises 15-18, classify the angle pair as corresponding. alternate interior, alternate exterior, or consecutive interior angles.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 23

Question 15.
∠5 and ∠1
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 15

Question 16.
∠11 and ∠13
Answer:

Question 17.
∠6 and ∠13
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 17

Question 18.
∠2 and ∠11
Answer:

ERROR ANALYSIS
In Exercises 19 and 20. describe and correct the error in the conditional statement about lines.

Question 19.
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Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 19

Question 20.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 25
Answer:

Question 21.
MODELING WITH MATHEMATICS
Use the photo to decide whether the statement is true or false. Explain Your reasoning.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 26
a. The plane containing the floor of the tree house is parallel to the ground.
b. The lines containing the railings of the staircase, such as Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 27, are skew to all lines in the plane containing the ground.
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 21

c. All the lines containing the balusters. such as Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 28, are perpendicular to the plane containing the floor of the tree house.
Answer:

Question 22.
THOUGHT PROVOKING
If two lines are intersected by a third line, is the third line necessarily a transversal? Justify your answer with a diagram.
Answer:

Question 23.
MATHEMATICAL CONNECTIONS
Two lines are cut by a transversal. Is it possible for all eight angles formed to have the same measure? Explain your reasoning.
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 23

Question 24.
HOW DO YOU SEE IT?
Think of each segment in the figure as part of a line.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 29
a. Which lines are parallel to Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 30?
b. Which lines intersect Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 30?
c. Which lines are skew to Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 30?
d. Should you have named all the lines on the cube in parts (a)-(c) except im – 30? Explain.
Answer:

In exercises 25-28. copy and complete the statement. List all possible correct answers.

Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 31

Question 25.
∠BCG and __________ are corresponding angles.
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 25

Question 26.
∠BCG and __________ are consecutive interior angles.
Answer:

Question 27.
∠FCJ and __________ are alternate interior angles.
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 27

Question 28.
∠FCA and __________ are alternate exterior angles.
Answer:

Question 29.
MAKING AN ARGUMENT
Your friend claims the uneven parallel bars in gymnastics are not really Parallel. She says one is higher than the other. so they cannot be in the same plane. Is she correct? Explain.

Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 29

Maintaining Mathematical Proficiency

Use the diagram to find the measure of all the angles.

Question 30.
m∠1 = 76°
Answer:

Question 31.
m∠2 = 159°
Answer:
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 3.1 a 31

3.2 Parallel Lines and Transversals

Exploration 1

Exploring parallel Lines

Work with a partner: Use dynamic geometry software to draw two parallel lines. Draw a third line that intersects both parallel lines. Find the measures of the eight angles that are formed. What can you conclude?
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 34
Answer:

Exploration 2

Writing conjectures

Work with a partner. Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal.
ATTENDING TO PRECISION
To be proficient in math, you need to communicate precisely with others.
a. corresponding angles
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 35
Answer:

b. alternate interior angles
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 36
Answer:

c. alternate exterior angles
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 37
Answer:

d. consecutive interior angles
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 38
Answer:

Communicate Your Answer

Question 3.
When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent?
Answer:

Question 4.
In Exploration 2. m∠1 = 80°. Find the other angle measures.
Answer:

Lesson 3.2 Parallel Lines and Transversals

Monitoring Progress

Use the diagram
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 39

Question 1.
Given m∠1 = 105°, find m∠4, m∠5, and m∠8. Tell which theorem you use in each case.
Answer:

Question 2.
Given m∠3 = 68° and m∠8 = (2x + 4)°, what is the value of x? Show your steps.
Answer:

Question 3.
In the proof in Example 4, if you use the third statement before the second statement. could you still prove the theorem? Explain.
Answer:

Question 4.
WHAT IF?
In Example 5. yellow light leaves a drop at an angle of m∠2 = 41°. What is m∠1? How do you know?
Answer:

Exercise 3.2 Parallel Lines and Transversals

Vocabulary and Core Concept Check

Question 1.
WRITING
How are the Alternate Interior Angles Theorem (Theorem 3.2) and the Alternate Exterior
Angles Theorem (Theorem 3.3) alike? How are they different?
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 1

Question 2.
WHICH ONE DOESN’T BELONG?
Which pair of angle measures does not belong with the other three? Explain.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 40
m∠1 and m∠3
m∠2 and m∠4
m∠2 and m∠3
m∠1 and m∠5
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3-6, find m∠1 and m∠2. Tell which theorem you use in each case.

Question 3.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 41
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 3

Question 4.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 42
Answer:

Question 5.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 43
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 5

Question 6.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 44
Answer:

In Exercises 7-10. find the value of x. Show your steps.

Question 7.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 45
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 7

Question 8.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 46
Answer:

Question 9.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 47
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 9

Question 10.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 48
Answer:

In Exercises 11 and 12. find m∠1, m∠2, and m∠3. Explain our reasoning.

Question 11.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 49
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 11

Question 12.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 50
Answer:

Question 13.
ERROR ANALYSIS
Describe and Correct the error in the students reasoning
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 51
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 13

Question 14.
HOW DO YOU SEE IT?
Use the diagram
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 52
a. Name two pairs of congruent angles when \(\ove
b. Name two pairs of supplementary angles when [latex]\overline{A B}\) and \(\overline{D C}\) are parallel. Explain your reasoning.
Answer:

PROVING A THEOREM
In Exercises 15 and 16, prove the theorem.

Question 15.
Alternate Exterior Angles Theorem (Thm. 3.3)
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 15

Question 16.
Consecutive Interior Angles Theorem (Thm. 3.4)
Answer:

Question 17.
PROBLEM SOLVING
A group of campers tie up their food between two parallel trees, as shown. The rope is pulled taut. forming a straight line. Find m∠2. Explain our reasoning.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 53
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 17

Question 18.
DRAWING CONCLUSIONS
You are designing a box like the one shown.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 54
a. The measure of ∠1 is 70°. Find m∠2 and m∠3.
b. Explain why ∠ABC is a straight angle.
c. If m∠1 is 60°, will ∠ABC still he a straight angle? Will the opening of the box be more steep or less steep? Explain.
Answer:

Question 19.
CRITICAL THINKING
Is it possible for consecutive interior angles to be congruent? Explain.
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 19

Question 20.
THOUGHT PROVOKING
The postulates and theorems in this book represent Euclidean geometry. In spherical geometry, all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. In spherical geometry, is it possible that a transversal intersects two parallel lines? Explain your reasoning.
Answer:

MATHEMATICAL CONNECTIONS
In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y.

Question 21.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 55
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 21

Question 22.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 56
Answer:

Question 23.
MAKING AN ARGUMENT
During a game of pool. your friend claims to be able to make the shot Shown in the diagram by hitting the cue ball so that m∠1 = 25°. Is your friend correct? Explain your reasoning.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 57
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 23

Question 24.
REASONING
In the diagram. ∠4 ≅∠5 and \(\overline{S E}\) bisects ∠RSF. Find m∠1. Explain your reasoning.
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 58
Answer:

Maintaining Mathematical Proficiency

Write the converse of the conditional statement. Decide whether it is true or false.

Question 25.
If two angles are vertical angles. then they are congruent.
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 25

Question 26.
If you go to the zoo, then you will see a tiger.
Answer:

Question 27.
If two angles form a linear pair. then they are supplementary.
Answer:
Big Ideas Math Answers Geometry Chapter 3 Parallel and Perpendicular Lines 3.2 a 27

Question 28.
If it is warm outside, then we will go to the park.
Answer:

3.3 Proofs with Parallel Lines

Exploration 1

Exploring Converses

Work with a partner: Write the converse of each conditional statement. Draw a diagram to represent the converse. Determine whether the converse is true. Justify your conclusion.
CONSTRUCTING VIABLE ARGUMENTS
To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures.

a. Corresponding Angles Theorem (Theorem 3.1): If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 59
Converse:
________________________________

________________________________

________________________________
Answer:

b. Alternate Interior Angles Theorem (Theorem 3.2): If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 60
Converse:
________________________________

________________________________

________________________________
Answer:

c. Alternate Exterior Angles Theorem (Theorem 3.3): If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 61
________________________________

________________________________

________________________________
Answer:

d. Consecutive Interior Angles Theorem (Theorem 3.4): If two parallel lines are cut by a transversal. then the pairs of consecutive interior angles are supplementary.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 62
________________________________

________________________________

________________________________
Answer:

Communicate Your Answer

Question 2.
For which of the theorems involving parallel lines and transversals is the converse true?
Answer:

Question 3.
In Exploration 1, explain how you would prove any of the theorems that you found to be true.
Answer:

Lesson 3.3 Proofs with Parallel Lines

Monitoring Progress

Question 1.
Is there enough information in the diagram to conclude that m || n? Explain.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 63
Answer:

Question 2.
Explain why the Corresponding Angles Converse is the converse of the Corresponding Angles Theorem (Theorem 3.1).
Answer:

Question 3.
If you use the diagram below to prove the Alternate Exterior Angles Converse. what Given and Prove statements would you use?
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 64
Answer:

Question 4.
Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2.

It is given that ∠4 ≅∠5. By the _______ . ∠1 ≅ ∠4. Then by the Transitive Property of Congruence (Theorem 2.2), _______ . So, by the _______ , g || h.
Answer:

Question 5.
Each step is parallel to the step immediately above it. The bottom step is parallel to the ground. Explain why the top step is parallel t0 the ground.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 65
Answer:

Question 6.
In the diagram below. p || q and q || r. Find m∠8. Explain your reasoning.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 66
Answer:

Exercise 3.3 Proofs with Parallel Lines

Vocabulary and Core Concept Check

Question 1.
VOCABULARY
Two lines are cut by a transversal. Which angle pairs must be congruent for the lines to be parallel?
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 1

Question 2.
WRITING
Use the theorems from Section 3.2 and the converses of those theorems in this section to write three biconditional statements about parallel lines and transversals.
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3-8. find the value of x that makes m || n. Explain your reasoning.

Question 3.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 67
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 3

Question 4.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 68
Answer:

Question 5.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 69
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 5

Question 6.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 70
Answer:

Question 7.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 71
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 7

Question 8.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 72
Answer:

In Exercises 9 and 10, use a compass and straightedge to construct a line through point P that is parallel to line m.

Question 9.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 73
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 9

Question 10.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 74
Answer:

PROVING A THEOREM
In Exercises 11 and 12. prove the theorem.
Question 11.
Alternate Exterior Angles Converse (Theorem 3.7)
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 11

Question 12.
Consecutive Interior Angles Converse (Theorem 3.8)
Answer:

In Exercises 13-18. decide whether there is enough information to prove that m || n. If so, state the theorem you would use.

Question 13.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 75
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 13

Question 14.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 76
Answer:

Question 15.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 77
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 15

Question 16.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 78
Answer:

Question 17.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 79
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 17

Question 18.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 80
Answer:

ERROR ANALYSIS
In Exercises 19 and 20, describe and correct the error in the reasoning.

Question 19.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 81
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 19

Question 20.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 82
Answer:

In Exercises 21-24. are Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 83 and Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 84 parallel? Explain your reasoning.

Question 21.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 85
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 21

Question 22.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 86
Answer:

Question 23.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 87
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 23

Question 24.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 88
Answer:

Question 25.
ANALYZING RELATIONSHIPS
The map shows part of Denser, Colorado, Use the markings on the map. Are the numbered streets parallel to one another? Explain your reasoning.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 89
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 25

Question 26.
ANALYZING RELATIONSHIPS
Each rung of the ladder is parallel to the rung directly above it. Explain why the top rung is parallel to the bottom rung.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 90
Answer:

Question 27.
MODELING WITH MATHEMATICS
The diagram of the control bar of the kite shows the angles formed between the Control bar and the kite lines. How do you know that n is parallel to m?
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 91
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 27

Question 28.
REASONING
Use the diagram. Which rays are parallel? Which rays arc not parallel? Explain your reasoning.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 92
Answer:

Question 29.
ATTENDING TO PRECISION
Use the diagram. Which theorems allow you to conclude that m || n? Select all that apply. Explain your reasoning.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 93
(A) Corresponding Angles Converse (Thm 3.5)
(B) Alternate Interior Angles Converse (Thm 3.6)
(C) Alternate Exterior Angles Converse (Thm 3.7)
(D) Consecutive Interior Angles Converse (Thm 3.8)
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 29

Question 30.
MODELING WITH MATHEMATICS
One way to build stairs is to attach triangular blocks to an angled support, as shown. The sides of the angled support are parallel. If the support makes a 32° angle with the floor, what must m∠1 so the top of the step will be parallel to the floor? Explain your reasoning.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 94
Answer:

Question 31.
ABSTRACT REASONING
In the diagram, how many angles must be given to determine whether j || k? Give four examples that would allow you to conclude that j || k using the theorems from this lesson.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 95
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 31

Question 32.
THOUGHT PROVOKING
Draw a diagram of at least two lines cut by at least one transversal. Mark you diagram so that it cannot be proven that any lines are parallel. Then explain how your diagram would need to change in order to prove that lines are parallel.
Answer:

PROOF
In Exercises 33-36, write a proof.

Question 33.
Given m∠1 = 115°, m∠2 = 65°
Prove m||n
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 96
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 33

Question 34.
Given ∠1 and ∠3 are supplementary.
Prove m||n
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 97
Answer:

Question 35.
Given ∠1 ≅ ∠2, ∠3 ≅ ∠4
Prove \(\overline{A B} \| \overline{C D}\)
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 98
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 35

Question 36.
Given a||b, ∠2 ≅ ∠3
Prove c||d
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 99
Answer:

Question 37.
MAKING AN ARGUMENT
Your classmate decided that Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 100 based on the diagram. Is your classmate correct? Explain your reasoning.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 101
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 37

Question 38.
HOW DO YOU SEE IT?
Are the markings on the diagram enough to conclude that any lines are parallel? If so. which ones? If not, what other information is needed?
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 102
Answer:

Question 39.
PROVING A THEOREM
Use these steps to prove the Transitive Property of Parallel Lines Theorem
a. Cops the diagram with the Transitive Property of Parallel Lines Theorem on page 141.
b. Write the Given and Prove statements.
c. Use the properties of angles formed by parallel lines cut by a transversal to prove the theorem.
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 39

Question 40.
MATHEMATICAL CONNECTIONS
Use the diagram
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 103
a. Find the value of x that makes p || q.
b. Find the value of y that makes r || s.
c. Can r be parallel to s and can p, be parallel to q at the same time? Explain your reasoning.
Answer:

Maintaining Mathematical Proficiency
Use the Distance Formula to find time distance between the two points.

Question 41.
(1, 3) and (- 2, 9)
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 41

Question 42.
(- 3, 7) and (8, – 6)
Answer:

Question 43.
(5, – 4) and (0, 8)
Answer:
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 3.3 a 43

Question 44.
(13, 1) and (9, – 4)
Answer:

3.1 – 3.3 Study Skills: Analyzing Your Errors

Mathematical Practices

Question 1.
Draw the portion of the diagram that you used to answer Exercise 26 on page 130.
Answer:

Question 2.
In Exercise 40 on page 144. explain how you started solving the problem and why you started that way.
Answer:

3.1 – 3.3 Quiz

Think of each segment in the diagram as part of a line. Which lines(s) or plane(s) contain point G and appear to fit the description?

Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 104

Question 1.
line(s) parallel to Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 105.
Answer:

Question 2.
line(s) perpendicular to Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 105.
Answer:

Question 3.
line(s) skew to Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 105.
Answer:

Question 4.
plane(s) parallel to plane ADE
Answer:

Identify all pairs of angles of the given type.

Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 106

Question 5.
consecutive interior
Answer:

Question 6.
alternate interior
Answer:

Question 7.
corresponding
Answer:

Question 8.
alternate exterior
Answer:

Find m∠1 and m∠2. Tell which theorem you use in each case.

Question 9.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 107
Answer:

Question 10.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 108
Answer:

Question 11.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 109
Answer:

Decide whether there is enough information to prove that m || n. If so, state the theorem you would use.

Question 12.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 110
Answer:

Question 13.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 111
Answer:

Question 14.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 112
Answer:

Question 15.
Cellular phones use bars like the ones shown to indicate how much signal strength a phone receives from the nearest service tower. Each bar is parallel to the bar directly next to it.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 113
a. Explain why the tallest bar is parallel to the shortest bar.
Answer:

b. Imagine that the left side of each bar extends infinitely as a line.
If m∠1 = 58°, then what is m∠2?
Answer:

Question 16.
The diagram shows lines formed on a tennis court.
Big Ideas Math Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines 114
a. Identify two pairs of parallel lines so that each pair is in a different plane.
Answer:

b. Identify two pairs of perpendicular lines.
Answer:

c. Identify two pairs of skew line
Answer:

d. Prove that ∠1 ≅ ∠2.
Answer:

3.4 Proofs with Perpendicular Lines

Exploration 1

Writing Conjectures

Work with a partner: Fold a piece of pair in half twice. Label points on the two creases. as shown.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 115
a. Write a conjecture about \(\overline{A B}\) and \(\overline{C D}\). Justify your conjecture.
Answer:

b. Write a conjecture about \(\overline{A O}\) and \(\overline{O B}\) Justify your conjecture.
Answer:

Exploration 2

Exploring a segment Bisector

Work with a partner: Fold and crease a piece of paper. as shown. Label the ends of the crease as A and B.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 116
a. Fold the paper again so that point A coincides with point B. Crease the paper on that fold.
Answer:

b. Unfold the paper and examine the four angles formed by the two creases. What can you conclude about the four angles?
Answer:

Exploration 3

Writing a conjecture

Work with a partner.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 117
a. Draw \(\overline{A B}\), as shown.
Answer:

b. Draw an arc with center A on each side of AB. Using the same compass selling, draw an arc with center B on each side \(\overline{A B}\). Label the intersections of the arcs C and D.
Answer:

c. Draw \(\overline{C D}\). Label its intersection with \(\overline{A B}\) as 0. Write a conjecture about the resulting diagram. Justify your conjecture.
CONSTRUCTING VIABLE ARGUMENTS
To be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures.
Answer:

Communicate Your Answer

Question 4.
What conjectures can you make about perpendicular lines?
Answer:

Question 5.
In Exploration 3. find AO and OB when AB = 4 units.
Answer:

Lesson 3.4 Proofs with Perpendicular Lines

Monitoring Progress

Question 1.
Find the distance from point E to Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 118
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 119
Answer:

Question 2.
Prove the Perpendicular Transversal Theorem using the diagram in Example 2 and the Alternate Exterior Angles Theorem (Theorem 3.3).
Answer:

Question 3.
Is b || a? Explain your reasoning.
Answer:

Question 4.
Is b ⊥ c? Explain your reasoning.
Answer:

Exercise 3.4 Proofs with Perpendicular Lines

Vocabulary and core Concept Check

Question 1.
COMPLETE THE SENTENCE
The perpendicular bisector of a segment is the line that passes through the _______________ of the segment at a _______________ angle.
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 1

Question 2.
DIFFERENT WORDS, SAME QUESTION
Which is different? Find “both” answers.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 120
Find the distance from point X to Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 121
Answer:

Find XZ
Answer:

Find the length of \(\overline{X Y}\)
Answer:

Find the distance from line l to point X.
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3 and 4. find the distance from point A to Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 122.

Question 3.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 123
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 3

Question 4.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 124
Answer:

CONSTRUCTION
In Exercises 5-8, trace line m and point P. Then use a compass and straightedge to construct a line perpendicular to line m through point P.

Question 5.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 125
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 5

Question 6.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 126
Answer:

Question 7.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 127
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 7

Question 8.
Math
Answer:

CONSTRUCTION
In Exercises 9 and 10, trace \(\overline{A B}\). Then use a compass and straightedge to construct the perpendicular bisector of \(\overline{A B}\)

Question 9.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 129
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 9

Question 10.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 130
Answer:

ERROR ANALYSIS
In Exercises 11 and 12, describe and correct the error in the statement about the diagram.
Question 11.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 131
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 11

Question 12.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 132
Answer:

PROVING A THEOREM
In Exercises 13 and 14, prove the theorem.
Question 13.
Linear Pair Perpendicular Theorem (Thm. 3. 10)
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 13

Question 14.
Lines Perpendicular to a Transversal Theorem (Thm. 3.12)
Answer:

PROOF
In Exercises 15 and 16, use the diagram to write a proof of the statement.

Question 15.
If two intersecting lines are perpendicular. then they intersect to form four right angles.
Given a ⊥ b
Prove ∠1, ∠2, ∠3, and ∠4 are right angles.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 133
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 15.1
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 15.2

Question 16.
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
Given \(\overrightarrow{B A}\) ⊥\(\vec{B}\)C
Prove ∠1 and ∠2 are complementary
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 134
Answer:

In Exercises 17-22, determine which lines, if any, must be parallel. Explain your reasoning.

Question 17.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 135
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 17

Question 18.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 136
Answer:

Question 19.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 139
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 19

Question 20.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 140
Answer:

Question 21.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 141
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 21

Question 22.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 142
Answer:

Question 23.
USING STRUCTURE
Find all the unknown angle measures in the diagram. Justify your answer for cacti angle measure.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 143
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 23

Question 24.
MAKING AN ARGUMENT
Your friend claims that because you can find the distance from a point to aline, you should be able to find the distance between any two lines. Is your friend correct? Explain your reasoning.
Answer:

Question 25.
MATHEMATICAL CONNECTIONS
Find the value of x when a ⊥ b and b || c.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 144
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 25

Question 26.
HOW DO YOU SEE IT?
You are trying to cross a stream from point A. Which point should you jump to in order to jump the shortest distance? Explain your reasoning.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 145
Answer:

Question 27.
ATTENDING TO PRECISION
In which of the following diagrams is \(\overline{A C}\) || \(\overline{B D}\) and \(\overline{A C}\) ⊥ \(\overline{C D}\)? Select all that apply.
(A) Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 146
(B) Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 147
(C) Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 148
(D) Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 149
(E) Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 150
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 27

Question 28.
THOUGHT PROVOKING
The postulates and theorems in this book represent Euclidean geometry. In spherical geometry, all points are points on the surface of a sphere. A line is a circle on the sphere whose diameter is equal to the diameter of the sphere. In spherical geometry. how many right angles are formed by two perpendicular lines? Justify your answer.
Answer:

Question 29.
CONSTRUCTION
Construct a square of side length AB
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 151
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 29

Question 30.
ANALYZING RELATIONSHIPS
The painted line segments that brain the path of a crosswalk are usually perpendicular to the crosswalk. Sketch what the segments in the ph0t0 would look like if they were perpendicular to the crosswalk. Which type of line segment requires less paint? Explain your reasoning.
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 152
Answer:

Question 31.
ABSTRACT REASONING
Two lines, a and b, are perpendicular to line c. Line d is parallel to line c. The distance between lines a and b is x meters. The distance between lines c and d is y meters. What shape is formed by the intersections of the four lines?
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 31

Question 32.
MATHEMATICAL CONNECTIONS
Find the distance between the lines with the equations y = \(\frac{3}{2}\) + 4 and – 3x + 2y = – 1.
Answer:

Question 33.
WRITING
Describe how you would find the distance from a point to a plane. Can you find the distance from a line to a plane? Explain your reasoning.
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 33

Maintaining Mathematical Proficiency

Simplify the ratio.

Question 34.
\(\frac{6-(-4)}{8-3}\)
Answer:

Question 35.
\(\frac{3-5}{4-1}\)
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 35

Question 36.
\(\frac{8-(-3)}{7-(-2)}\)
Answer:

Question 37.
\(\frac{13-4}{2-(-1)}\)
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 37

Identify the slope and they y-intercept of the line.

Question 38.
y = 3x + 9
Answer:

Question 39.
y = –\(\frac{1}{2}\)x + 7
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 39

Question 40.
y = \(\frac{1}{6}\)x – 8
Answer:

Question 41.
y = – 8x – 6
Answer:
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 3.4 a 41

3.5 Equations of Parallel and Perpendicular Lines

Exploration 1

Writing Equations of Parallel and Perpendicular Lines

Work with a partner: Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. Use a graphing calculator to verify your answer. What is the relationship between the slopes?
a.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 153
Answer:

b.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 154
Answer:

c.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 155
Answer:

d.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 156
Answer:

e.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 157
Answer:

f.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 158
Answer:

Exploration 2

Writing Equations of Parallel and Perpendicular Lines

Work with a partner: Write the equations of the parallel or perpendicular lines. Use a graphing calculator to verify your answers.

a.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 159
Answer:

b.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 160
Answer:

Communicate Your Answer

Question 3.
How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point?
MODELING WITH MATHEMATICS
To be proficient in math, you need to analyze relationships mathematically to draw conclusions.
Answer:

Question 4.
Write an equation of the line that is (a) parallel and (b) perpendicular to the line y = 3x + 2 and passes through the point (1, -2).
Answer:

Lesson 3.5 Equations of Parallel and Perpendicular Lines

Monitoring Progress

Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.

Question 1.
A(1, 3), B(8, 4); 4 to 1
Answer:

Question 2.
A(- 2, 1), B(4, 5); 3 to 7
Answer:

Question 3.
Determine which of the lines are parallel and which of the lines are perpendicular.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 161
Answer:

Question 4.
Write an equation of the line that passes through the point (1, 5) and is
(a) parallel to the line y = 3x – 5 and
Answer:

(b) perpendicular to the line y = 3x – 5.
Answer:

Question 5.
How do you know that the lines x = 4 and y = 2 are perpendicular?
Answer:

Question 6.
Find the distance from the point (6, 4) to the line y = x + 4.
Answer:

Question 7.
Find the distance from the point (- 1, 6) to the line y = – 2x.
Answer:

Exercise 3.5 Equations of Parallel and Perpendicular Lines

Vocabulary and Core Concept Check

Question 1.
COMPLETE THE SENTENCE
A _________ line segment AB is a segment that represents moving from point A to point B.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 1

Question 2.
WRITING
How are the slopes of perpendicular lines related?
Answer:

Monitoring Progress and Modeling with Mathematics

In Exercises 3 – 6. find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.

Question 3.
A(8, 0), B(3, – 2); 1 to 4
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 3

Question 4.
A(- 2, – 4), B(6, 1); 3 to 2
Answer:

Question 5.
A(1, 6), B(- 2, – 3); 5 to 1
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 5

Question 6.
A(- 3, 2), B(5, – 4); 2 to 6
Answer:

In Exercises 7 and 8, determine which of the lines are parallel and which of the lines are perpendicular.

Question 7.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 162
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 7

Question 8.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 163
Answer:

In Exercises 9 – 12, tell whether the lines through the given points are parallel, perpendicular, or neither. justify your answer.

Question 9.
Line 1: (1, 0), (7, 4)
Line 2: (7, 0), (3, 6)
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 9

Question 10.
Line 1: (- 3, 1), (- 7, – 2)
Line 2: (2, – 1), (8, 4)
Answer:

Question 11.
Line 1: (- 9, 3), (- 5, 7)
Line 2: (- 11, 6), (- 7, 2)
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 11

Question 12.
Line 1: (10, 5), (- 8, 9)
Line 2: (2, – 4), (11, – 6)
Answer:

In Exercises 13 – 16. write an equation of the line passing through point P that ¡s parallel to the given line. Graph the equations of the lines to check that they are parallel.

Question 13.
P(0, – 1), y = – 2 + 3
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 13

Question 14.
P(3, 8), y = \(\frac{1}{5}\)(x + 4)
Answer:

Question 15.
P(- 2, 6), x = – 5
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 15

Question 16.
P(4, 0), – x + 2y = 12
Answer:

In Exercises 17 – 20. write an equation of the line passing through point P that is perpendicular to the given line. Graph the equations of the lines to check that they are perpendicular.

Question 17.
P(0, 0), y = – 9x – 1
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 17

Question 18.
P(4, – 6)y = – 3
Answer:

Question 19.
P(2, 3), y – 4 = – 2(x + 3)
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 19.1
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 19.2

Question 20.
P(- 8, 0), 3x – 5y = 6
Answer:

In Exercises 21 – 24, find the distance from point A to the given line.

Question 21.
A(- 1, 7), y = 3x
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 21.1
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 21.2

Question 22.
A(- 9, – 3), y = x – 6
Answer:

Question 23.
A(15, – 21), 5x + 2y = 4
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 23.1
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 23.2

Question 24.
A(- \(\frac{1}{4}\), 5), – x + 2y = 14
Answer:

Question 25.
ERROR ANALYSIS
Describe and correct the error in determining whether the lines are parallel. perpendicular, or neither.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 164
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 25

Question 26.
ERROR ANALYSIS
Describe and correct the error in writing an equation of the line that passes through the point (3, 4) and is parallel to the line y = 2x + 1.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 165
Answer:

In Exercises 27-30. find the midpoint of \(\overline{P Q}\). Then write
an equation of the line that passes through the midpoint and is perpendicular to \(\overline{P Q}\). This line is called the perpendicular bisector.

Question 27.
P( – 4, 3), Q(4, – 1)
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 27

Question 28.
P(- 5, – 5), Q(3, 3)
Answer:

Question 29.
P(0, 2), Q(6, – 2)
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 29

Question 30.
P(- 7, 0), Q(1, 8)
Answer:

Question 31.
MODELING WITH MATHEMATICS
Your school lies directly between your house and the movie theater. The distance from your house to the school is one-fourth of the distance from the school to the movie theater. What point on the graph represents your school?
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 166
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 31

Question 32.
REASONING
Is quadrilateral QRST a parallelogram? Explain your reasoning.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 167
Answer:

Question 33.
REASONING
A triangle has vertices L(0, 6), M(5, 8). and N(4, – 1), Is the triangle a right triangle? Explain ‘your reasoning.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 33

Question 34.
MODELING WITH MATHEMATICS
A new road is being constructed parallel to the train tracks through points V. An equation of the line representing the train tracks is y = 2x. Find an equation of the line representing the new road.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 168
Answer:

Question 35.
MODELING WITH MATHEMATICS
A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). An equation of the line representing Washington Boulevard is y = –\(\frac{2}{3}\)x. Find an equation of the line representing the bike path.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 169
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 35

Question 36.
PROBLEM SOLVING
A gazebo is being built near a nature trail. An equation of the line representing the nature trail is y = \(\frac{1}{3}\)x – 4. Each unit in the coordinate plane corresponds to 10 feet. Approximately how far is the gazebo from the nature trail?
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 170
Answer:

Question 37.
CRITICAL THINKING
The slope of line l is greater than 0 and less than 1. Write an inequality for the slope of a line perpendicular to l. Explain your reasoning.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 37

Question 38.
HOW DO YOU SEE IT?
Determine whether quadrilateral JKLM is a square. Explain your reasoning.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 171
Answer:

Question 39.
CRITICAL THINKING
Suppose point P divides the directed line segment XY So that the ratio 0f XP to PY is 3 to 5. Describe the point that divides the directed line segment YX so that the ratio of YP Lo PX is 5 to 3.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 39

Question 40.
MAKING AN ARGUMENT
Your classmate claims that no two nonvertical parallel lines can have the same y-intercept. Is your classmate correct? Explain.
Answer:

Question 41.
MATHEMATICAL CONNECTIONS
Solve each system of equations algebraically. Make a conjecture about what the solution(s) can tell you about whether the lines intersect. are parallel, or are the same line.
a. y = 4x + 9
4x – y = 1
b. 3y + 4x = 16
2x – y = 18
c. y = – 5x + 6
10x + 2y = 12
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 41.1
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 41.2

Question 42.
THOUGHT PROVOKING
Find a formula for the distance from the point (x0 V0) to the line ax + by = 0. Verify your formula using a point and a line.
Answer:

MATHEMATICAL CONNECTIONS
In Exercises 43 and 44, find a value for k based on the given description.

Question 43.
The line through (- 1, k) and (- 7, – 2) is parallel to the line y = x + 1.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 43

Question 44.
The line through (k, 2) and (7, 0) is perpendicular to the line y = x – \(\frac{28}{5}\).
Answer:

Question 45.
ABSTRACT REASONING
Make a conjecture about how to find the coordinates of a point that lies beyond point B along \(\vec{A}\)B. Use an example to support your conjecture.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 45

Question 46.
PROBLEM SOLVING
What is the distance between the lines y = 2x and y = 2x + 5? Verify your answer.
Answer:

PROVING A THEOREM
In Exercises 47 and 48, use the slopes of lines to write a paragraph proof of the theorem.

Question 47.
Lines Perpendicular to a Transversal Theorem (Theorem 3.12): In a plane. if two lines are perpendicular to the same line. then they are parallel to each other.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 47

Question 48.
Transitive Property of Parallel Lines Theorem (Theorem 3.9): If two lines are parallel to the same line, then they are parallel to each other.
Answer:

Question 49.
PROOF
Prove the statement: If two lines are vertical. then they are parallel.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 49

Question 50.
PROOF
Prove the statement: If two lines are horizontal, then they are parallel.
Answer:

Question 51.
PROOF
Prove that horizontal lines are perpendicular to vertical lines.
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 51

Maintaining Mathematical Proficiency

Plot the point in a coordinate plane.

Question 52.
A(3, 6)
Answer:

Question 53.
B(0, – 4)
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 53

Question 54.
C(5, 0)
Answer:

Question 55.
D( – 1, – 2)
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 55

Copy and complete the table.

Question 56.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 172
Answer:

Question 57.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 173
Answer:
Big Ideas Math Geometry Solutions Chapter 3 Parallel and Perpendicular Lines 3.5 a 57

3.4 – 3.5 Performance Task: Navajo Rugs

Mathematical Practices

Question 1.
Compare the effectiveness of the argument in Exercise 24 on page 153 with the argument “You can find the distance between any two parallel lines” What flaw(s) exist in the argument(s)? Does either argument use correct reasoning? Explain.
Answer:

Question 2.
Look back at your construction of a square in Exercise 29 on page 154. How would your
construction change if you were to construct a rectangle?
Answer:

Question 3.
In Exercise 31 on page 161, a classmate tells you that our answer is incorrect because you should have divided the segment into four congruent pieces. Respond to your classmates argument by justifying your original answer.
Answer:

Parallel and Perpendicular Lines Chapter Review

3.1 Pairs of Lines and Angles

Think of each segment in the figure as part of a line. Which line(s) or plane(s) appear to fit the description?
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 174
Question 1.
line(s) perpendicular to Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 175
Answer:

Question 2.
line(s) parallel to Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 175
Answer:

Question 3.
line(s) skew to Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 175
Answer:

Question 4.
plane(s) parallel to plane LMQ
Answer:

3.2 Parallel Lines and Transversals

Find the values of x and y.

Question 5.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 176
Answer:

Question 6.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 177
Answer:

Question 7.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 178
Answer:

Question 8.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 179
Answer:

3.3 Proofs with Parallel Lines

Find the value of x that makes m || n.

Question 9.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 180
Answer:

Question 10.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 181
Answer:

Question 11.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 182
Answer:

Question 12.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 183
Answer:

3.4 Proofs with Perpendicular Lines

Determine which lines, if any, must be parallel. Explain your reasoning.

Question 13.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 184
Answer:

Question 14.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 185
Answer:

Question 15.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 186
Answer:

Question 16.
Big Ideas Math Answer Key Geometry Chapter 3 Parallel and Perpendicular Lines 187
Answer:

3.5 Equations of Parallel and Perpendicular Lines

Write an equation of the line passing through the given point that is parallel to the given line.

Question 17.
A(3, – 4),y = – x + 8
Answer:

Question 18.
A(- 6, 5), y = \(\frac{1}{2}\)x – 7
Answer:

Question 19.
A(2, 0), y = 3x – 5
Answer:

Question 20.
A(3, – 1), y = \(\frac{1}{3}\)x + 10
Answer:

Write an equation of the line passing through the given point that is perpendicular to the given line.

Question 21.
A(6, – 1), y = – 2x + 8
Answer:

Question 22.
A(0, 3), y = – \(\frac{1}{2}\)x – 6
Answer:

Question 23.
A(8, 2),y = 4x – 7
Answer:

Question 24.
A(-1, 5), y = \(\frac{1}{7}\)x + 4
Answer:

Find the distance front point A to the given line.

Question 25.
A(2, – 1), y = – x + 4
Answer:

Question 26.
A(- 2, 3), y = \(\frac{1}{2}\)x + 1
Answer:

Parallel and Perpendicular Lines Test

Find the values of x and y. State which theorem(s) you used.

Question 1.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 188
Answer:

Question 2.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 189
Answer:

Question 3.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 190
Answer:

Find the distance from point A to the given line.

Question 4.
A(3, 4), y = – x
Answer:

Question 5.
A(- 3, 7), y = \(\frac{1}{3}\)x – 2
Answer:

Find the value of x that makes m || n.

Question 6.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 191
Answer:

Question 7.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 192
Answer:

Question 8.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 193
Answer:

Write an equation of the line that passes through the given point and is
(a) parallel to and
(b) perpendicular to the given line.

Question 9.
(- 5, 2), y = 2x – 3
Answer:

Question 10.
(- 1, – 9), y = – \(\frac{1}{3}\)x + 4
Answer:

Question 11.
A student says. “Because j ⊥ K, j ⊥ l’ What missing information is the student assuming from the diagram? Which theorem is the student trying to use?
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 194
Answer:

Question 12.
You and your family are visiting some attractions while on vacation. You and our your mom visit the shopping mall while your dad and your sister visit the aquarium. You decide to meet at the intersection of lines q and p. Each unit in the coordinate plane corresponds to 50 yards.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 195

a. Find an equation of line q.
Answer:

b. Find an equation of line p.
Answer:

c. What are the coordinates of the meeting point?
Answer:

d. What is the distance from the meeting point to the subway?
Answer:

Question 13.
Identify an example on the puzzle cube of each description. Explain your reasoning.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 196
a. a pair of skew lines
Answer:

b. a pair of perpendicular lines
Answer:

c. a pair of partlIeI lines
Answer:

d. a pair of congruent corresponding angles
Answer:

e. a pair of congruent alternate interior angles
Answer:

Parallel and Perpendicular Lines Cumulative Assessment

Question 1.
Use the steps in the construction to explain how you know that im – 197 is the perpendicular bisector of \(\overline{A B}\).
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 198
Answer:

Question 2.
The equation of a line is x + 2y = 10.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 199
a. Use the numbers and symbols to create the equation of a line in slope-intercept form
that passes through the point (4, – 5) and is parallel to the given line.
Answer:

b. Use the numbers and symbols to create the equation of a line in slope-intercept form
that passes through the point (2, – 1) and is perpendicular to the given line.
Answer:

Question 3.
Classify each pair of angles whose measurements are given.
a.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 200
Answer:

b.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 201
Answer:

c.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 202
Answer:

d.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 203
Answer:

Question 4.
Your school is installing new turf on the football held. A coordinate plane has been superimposed on a diagram of the football field where 1 unit = 20 feet.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 204
a. What is the length of the field?
Answer:

b. What is the perimeter of the field?
Answer:

c. Turf costs $2.69 per square foot. Your school has a $1,50,000 budget. Does the school have enough money to purchase new turf for the entire field?
Answer:

Question 5.
Enter a statement or reason in each blank to complete the two-column proof.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 205
Given ∠1 ≅∠3
Prove ∠2 ≅∠4
Table – 1
Answer:

Question 6.
Your friend claims that lines m and n are parallel. Do you support your friend’s claim? Explain your reasoning.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 206
Answer:

Question 7.
Which of the following is true when Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 207 are skew?
(A) Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 207 are parallel.
(B) Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 207 intersect
(C) Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 207 are perpendicular
(D) A, B, and C are noncollinear.
Answer:

Question 8.
Select the angle that makes the statement true.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 208
∠1    ∠2    ∠3    ∠4    ∠5     ∠6     ∠7     ∠8
a. ∠4 ≅ ________ b the Alternate Interior Angles Theorem (Thm. 3.2).
Answer:

b. ∠2 ≅ ________ by the Corresponding Angles Theorem (Thm. 3. 1)
Answer:

c. ∠1 ≅ ________ by the Alternate Exterior Angles Theorem (Thm. 3.3).
Answer:

d. m∠6 + m ________ = 180° by the Consecutive Interior Angles Theorem (Thm. 3.4).
Answer:

Question 9.
You and your friend walk to school together every day. You meet at the halfway point between your houses first and then walk to school. Each unit in the coordinate plane corresponds to 50 yards.
Big Ideas Math Geometry Answers Chapter 3 Parallel and Perpendicular Lines 209
a. What are the coordinates of the midpoint of the line segment joining the two houses?
Answer:

b. What is the distance that the two of you walk together?
Answer:

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