We included HMH Into Math Grade 7 Answer Key PDF Module 9 Lesson 4 Draw and Analyze Shapes to Solve Problems to make students experts in learning maths.
HMH Into Math Grade 7 Module 9 Lesson 4 Answer Key Draw and Analyze Shapes to Solve Problems
I Can use tools to draw or construct figures that meet given criteria, and I can analyze the resulting figures.
Step It Out
Question 1.
Lucas is using strips of wood to construct a triangle. The first two strips are 4 feet long and 7 feet long. When Lucas nails them together, the two pieces of wood form a 50° angle.
A. Draw a model of the two strips after Lucas nailed them together.
Answer:
B. Can he use a third strip to construct a triangle? If so, complete the model.
Answer:
Yes, he can use third strip to construct a triangle.
C. How many triangles can be formed?
Answer:
Only one triangle can be formed for the given details.
Explanation:
From the given information Lucas has the first two strips are 4 feet long and 7 feet long.
When Lucas nails them together, the two pieces of wood form a 50° angle.
So, he can form only one triangle.
Question 2.
In this task, you will draw triangles given the lengths of two sides and the measure of an angle that is not between them.
A. Side AB: 8 units; Side BC 6 units; Angle A: 40°
To construct Triangle ABC, you need to draw Side BC. Because Side BC is 6 units long, put the point of the compass at Point 6 and draw part of a circle with radius 6 units. You can use this segment to help you open your compass to the correct radius.
The circle intersects the other side of ∠A in ___________ point(s). You can draw _________ triangle(s). Draw the triangle(s).
Answer:
The circle intersects the other side of ∠A in ___________ point(s).
Explanation:
Given information is Side AB: 8 units; Side BC 6 units; Angle A: 40°
The circle intersects the other side of ∠A in two point(s) C1 and C2.
B. Side AB: 5 units; Side BC: 7 units; Angle A: 90°
To draw Side BC, put the point of the compass on Point B, and draw part of a circle with radius 7 units. Use this 7-unit segment to open your compass to the correct radius.
The circle intersects the other side of ∠A at __________ point(s).
You can draw __________ triangle(s). Draw the triangle(s).
Answer:
Explanation:
The circle intersects the other side of ∠A at one point C.
C. Side AB: 6 units; Side BC: 9 units; Angle A: 120°
Use this segment to help you draw Side BC.
The circle intersects the other side of ∠A at point(s). You can draw ________ triangle(s). Draw the triangle(s).
Answer:
Explanation:
The circle intersects the other side of ∠A at one point C.
D. How many triangles did you draw in Parts A-C given two sides and the measure of an angle that is not between them?
Answer:
four triangles can be drawn as shown in above pictures.
Turn and Talk How are the situations in Step It Out 1 and Step It Out 2 different? How are they the same?
Answer:
As, the angle between the two lines and radius increases, the number of cuts will decreases.
we observed, for larger angle and foe smaller angle and smaller units length and larger units length.
Check Understanding
Question 1.
Draw a right triangle with two sides of lengths 4 units and 5 units and the 90° angle between them.
Answer:
Explanation:
The sum of the two sides of a triangle is greater than the third side.
So, 4 + 5 = 9
So, the third side should be less than 9 units.
The sum of the internal angles is 180 degrees.
Question 2.
Draw a right triangle with two sides of lengths 4 units and 5 units with the 90° angle not between them.
Answer:
Explanation:
The sum of the two sides of a triangle is greater than the third side.
So, 4 + 5 = 9
So, the third side should be less than 9 units.
The sum of the internal angles is 180 degrees.
On Your Own
Question 3.
A triangle with the largest possible base is drawn inside a circle. What part of the circle must coincide with the base of the triangle?
Answer:
BC of the circle must coincide with the base of the triangle.
Explanation:
The largest possible base is drawn inside a circle is the diameter of the circle BC
sides of length diameter can form a triangle as shown below picture.
Question 4.
Use Tools Use the diagram shown. Construct two different triangles that each have Side AB with a length of 8 units, Side BC with a length of 5 units, and a 35° angle that is not between them. Use the segment below to help you draw Side BC.
Answer:
Explanation:
By using compass cut the base with radius with 5 units length as shown below
the base is cut at two points C and D
using protractor measure the angles formed at C and D are same 70° and angle B is 40° for triangle BCD and 40° for triangle ABC.
Question 5.
STEM An ethologist is a scientist who studies animal behavior. One ethologist studied the play behavior of a group of infant lowland gorillas and measured the portion of play time given to three types of play. Draw a circle graph to show the portion of the day for each type. The measure of the angle between the sides of the section for each behavior is given.
Solitary play: 150°
Social play: 195°
Mother-infant play: 15°
Answer:
Explanation:
The sum of the internal angles in a circle is 180 degrees.
So, 150° + 195° + 5° = 360°
Question 6.
Travis draws a triangle with three 60° angles and three sides of length 5 inches.
A. Can Margarita draw a triangle with the same angle measures as Travis’s triangle but with different side lengths? Why or why not?
Answer:
No, she cannot draw.
Explanation:
Travis draws a triangle with three 60° angles and three sides of length 5 inches is an equilateral triangle as shown below, but Margarita has the same angle measures with different side lengths. So, she cannot draw the same triangle as her.
B. Can she draw a triangle with the same side lengths as Travis’s triangle but with different angle measures? Explain.
Answer:
Its an equilateral triangle with same side lengths and same angle 60° as shown above.
Explanation:
An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a “regular” triangle.
Question 7.
Use Tools Students were surveyed about the number of siblings they have. Draw a circle graph to show the part of the group surveyed that has each given number of siblings. The table shows the measure of the angle between the sides of the section for each number of siblings.
Answer:
Explanation:
The sum of the internal angles in a circle is 180 degrees.
So, 40° + 40° + 50° + 50° + 85° + 95° = 360°
Question 8.
Use Tools Draw a triangle that has two sides of lengths 7 units and 5 units with a 42° angle between them. Can you draw more than one triangle?
Answer:
Yes, as shown in the figure below we can draw more than one triangle.
Explanation:
The sum of the two sides is greater than the third side.
So, 7 + 5 = 12 units
The sum of the internal angles in triangle is 180 degrees.
Question 9.
Open-Ended Draw a figure that has at least one pair of parallel sides and at least one side that is 6 units long. The figure should also have at least one line of symmetry.
Answer:
Quadrilateral
Explanation:
Quadrilateral is a simple polygon with four sides, four vertex and four angles.
A pair of sides in the quadrilateral is parallel to each other with symmetry as shown in the above figure.
Lesson 9.4 More Practice/Homework
Question 1.
Open-Ended Draw a figure that has at least one pair of perpendicular sides, at least one side that is 4 units long, and at least one line of symmetry.
Answer:
Explanation:
The above figure shows one pair of perpendicular sides, at least one side that is 4 units long, and at least one line of symmetry.
ABCD is Open-Ended figure that has pair of perpendicular sides AB & BC and BC & DC.
BC side that is 4 units long, and at least one line of symmetry green line.
Question 2.
Use Tools How many triangles can you draw that have two sides of lengths 5 units and 2 units and a 68° angle between them? Draw the triangle(s).
Answer:
Only one triangle
Explanation:
The sum of the two sides is greater than the third side.
So, 2 + 5 = 7units
The sum of the internal angles in triangle is 180 degrees.
Question 3.
A. Use Tools Complete the drawing to make Triangle(s) ABC with Side AB of length 9 units, Side BC of length 7 units, and Angle A with measure 45°. Use this segment to help you draw side BC.
Answer:
B. How many triangles with these measurements can you draw?
Answer:
Two triangles
Explanation:
The sum of the two sides is greater than the third side.
So, 7 + 9 = 16 units
The sum of the internal angles in triangle is 180 degrees.
Question 4.
Reason The two longest sides of a triangle are 7 inches and 10 inches long. Describe a possible length for the shortest side. Explain your reasoning.
Answer:
the possible length of third side is 17< x > 3 inches
Explanation:
The sum of the two sides is greater than the third side.
c + 7 = 10
c = 10 – 7 = 3
c should be more than 3 to form a triangle.
Test Prep
Question 5.
Indicate whether one, no, or many triangles can be drawn with the given side lengths and/or angle measures.
Answer:
Explanation:
The sum of the two sides is greater than the third side.
The sum of the internal angles in triangle is 180 degrees.
Question 6.
A triangle has two sides of lengths 20 centimeters and 8 centimeters. Which can be the length of the third side of the triangle? Select all that apply.
(A) 30 centimeters
(B) 22 centimeters
(C) 14 centimeters
(D) 8 centimeters
(E) 6 centimeters
Answer:
Option(A)
Explanation:
AB + BC => AC
The sum of the length of the two sides of a triangle is greater than the length of the third side.
20 + 8 = 28 cm
In the same way, the difference between the two sides of a triangle is less than the length of the third side.
20 – 8 = 12 cm
Question 7.
A road worker wants to place a circular map on a square sign that has a perimeter of 240 inches. What is the greatest possible radius of the circular map?
(A) 15 inches
(B) 30 inches
(C) 60 inches
(D) 120 inches
Answer:
Option (B)
Explanation:
perimeter of a square is 240 inches
Side = P/4 = 240/4 = 60 in
Diameter is 60 in
r = d/2 = 60/2 = 30in
the greatest possible radius of the circular map is 30 in
Spiral Review
Question 8.
It has been raining for hours, and 0.75 inch of rain has fallen. If there are 1.5 inches of rain in a single storm, Carmen knows that the basement of the building she is in will flood. The rain begins falling at a rate of 0.175 inch per hour! Write an inequality to represent how long it can continue to rain at this rate before the basement floods.
Answer:
Rate of rainfall is 4.28 cm
need 4hrs 28 min to fill the basement.
Explanation:
Inches of rain the basement will flood in = 1.5 inch
Inches of rain which has already fallen = 0.75 inch
Remaining Inches of rain which will fall for the basement to flood in = 1.5 – 0.75
= 0.75 inches of rain
Rate of rain fall = 0.175 per hour
Time taken for the rain to fill the basement = Remaining Inches of rain ÷ Rate of rain fall
= 0.75 ÷ 0.175
= 4.28
Time taken for the rain to fill the basement = 4 hours 28 minutes
Question 9.
Two complementary angles have measures of (4x + 5)° and (2x + 7)°. What is the value of x? What are the measures of the angles?
Answer:
13.5°
Explanation:
Two complementary angles have measures of (4x + 5)° and (2x + 7)°
(4x + 5)° + (2x + 7)° = 90°
6x + 9 = 90
6x = 90 – 9
6x = 81
x = 13.5°