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## Go Math Grade 4 Chapter 10 Two-Dimensional Figures Answer Key

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Lesson 1: Lines, Rays, and Angles

Lesson 2: Classify Triangles by Angles

- Classify Triangles by Angles – Page No. 557
- Classify Triangles by Angles Lesson Check – Page No. 558
- Classify Triangles by Angles Lesson Check 1 – Page No. 559
- Classify Triangles by Angles Lesson Check 2 – Page No. 560

Lesson 3: Parallel Lines and Perpendicular Lines

- Parallel Lines and Perpendicular Lines – Page No. 563
- Parallel Lines and Perpendicular Lines Lesson Check – Page No. 564
- Parallel Lines and Perpendicular Lines Lesson Check 1 – Page No. 565
- Parallel Lines and Perpendicular Lines Lesson Check 2 – Page No. 566

Lesson 4: Classify Quadrilaterals

- Classify Quadrilaterals – Page No. 569
- Classify Quadrilaterals Lesson Check – Page No. 570
- Classify Quadrilaterals Lesson Check 1 – Page No. 571
- Classify Quadrilaterals Lesson Check 2 – Page No. 572

Mid-Chapter Checkpoint

Lesson 5: Line Symmetry

- Line Symmetry – Page No. 577
- Line Symmetry Lesson Check – Page No. 578
- Line Symmetry Lesson Check 1 – Page No. 579
- Line Symmetry Lesson Check 2 – Page No. 580

Lesson 6: Find and Draw Lines of Symmetry

- Find and Draw Lines of Symmetry – Page No. 583
- Find and Draw Lines of Symmetry Lesson Check – Page No. 584
- Find and Draw Lines of Symmetry Lesson Check 1 – Page No. 585
- Find and Draw Lines of Symmetry Lesson Check 2 – Page No. 586

Lesson 7: Problem Solving • Shape Patterns

- Shape Patterns – Page No. 589
- Shape Patterns Lesson Check – Page No. 590
- Shape Patterns Lesson Check 1 – Page No. 591
- Shape Patterns Lesson Check 2 – Page No. 592
- Shape Patterns Lesson Check 3 – Page No. 593

Review/Test

- Review/Test – Page No. 594
- Review/Test – Page No. 595
- Review/Test – Page No. 596
- Review/Test – Page No. 597
- Review/Test – Page No. 598
- Review/Test – Page No. 603
- Review/Test – Page No. 604

### Common Core – New – Page No. 553

**Lines, Rays, and Angles
**

**Draw and label an example of the figure.**

Question 1.

obtuse ∠ABC

Think: An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.

_________

Answer:

Explanation:

An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.

Question 2.

\(\overrightarrow{G H}\)

_________

Answer:

Explanation:

GH is a ray that has one endpoint and continues without an end in one direction.

Question 3.

acute ∠JKL

_________

Answer:

Explanation:

Angle JKL is an acute angle that is less than a right angle.

Question 4.

\(\overline{B C}\)

Answer:

Explanation:

BC is a line that continues without an end in both directions.

**Use the figure for 5–8.**

Question 5.

Name a line segment.

Answer:

line segment EF

Explanation:

EF line is a straight path of points that continues without an end in both directions.

Question 6.

Name a right angle.

∠ _____

Answer:

∠EJF

Explanation:

EJF is a right angle that forms a square corner.

Question 7.

Name an obtuse angle.

obtuse ∠ _____

Answer:

∠CEJ

Explanation:

CEJ is an obtuse angle that is greater than a right angle.

Question 8.

Name a ray.

Answer:

Ray JD

Explanation:

JD is a ray that has one endpoint and continues without an end in one direction.

**Problem Solving**

**Use the figure at the right for 9–11.**

Question 9.

Classify ∠AFD

_________

Answer:

Obtuse Angle

Explanation:

AFD is an obtuse angle that is greater than a right angle.

Question 10.

Classify ∠CFE.

_________

Answer:

Right Angle

Explanation:

∠CFE is a right angle that forms a square corner.

Question 11.

Name two acute angles.

acute ∠ _____ acute ∠ _____

Answer:

∠AFB and ∠DFE

Explanation:

∠AFB and ∠DFE are two acute angles with less than a right angle.

### Common Core – New – Page No. 554

**Lesson Check**

Question 1.

The hands of a clock show the time 12:25.

Which best describes the angle between the hands of the clock?

Options:

a. acute

b. right

c. obtuse

d. straight

Answer:

c. obtuse

Explanation:

The hands of the time 12:25 are forming greater than a right angle. So, the answer is the Obtuse angle.

Question 2.

Which of the following name two different figures?

Options:

a. \(\overline{A B} \text { and } \overline{B A}\)

b. \(\stackrel{\longleftrightarrow}{A B}\) and \(\stackrel{\longleftrightarrow}{B A}\)

c. \(\overrightarrow{A B} \text { and } \overrightarrow{B A}\)

d. ∠ABC and ∠CBA

Answer:

c. \(\overrightarrow{A B} \text { and } \overrightarrow{B A}\)

Explanation:

In \(\overrightarrow{A B}\), A is an end point and B continues without end in one direction.

In \(\overrightarrow{B A}\), B is an end point and A continues without an end in one direction.

**Spiral Review**

Question 3.

Jan’s pencil is 8.5 cm long. Ted’s pencil is longer. Which could be the length of Ted’s pencil?

Options:

a. 0.09 cm

b. 0.8 cm

c. 8.4 cm

d. 9.0 cm

Answer:

d. 9.0 cm

Explanation:

9 ones is greater than 8 ones. So, 9.0 cm > 8.5 cm

Question 4.

Kayla buys a shirt for $8.19. She pays with a $10 bill. How much change should she receive?

Options:

a. $1.81

b. $1.89

c. $2.19

d. $2.81

Answer:

a. $1.81

Explanation:

Kayla buys a shirt for $8.19. She pays with a $10 bill. To find the change she received, $10 – $8.19 = 1.81

Question 5.

Sasha donated \(\frac{9}{100}\) of her class’s entire can collection for the food drive. Which decimal is equivalent to \(\frac{9}{100}\) ?

Options:

a. 9

b. 0.99

c. 0.9

d. 0.09

Answer:

d. 0.09

Explanation:

\(\frac{9}{100}\) is 9 hundredths. So, the decimal is 0.09.

Question 6.

Jose jumped 8 \(\frac{1}{3}\) feet. This was 2 \(\frac{2}{3}\) feet farther than Lila jumped. How far did Lila jump?

Options:

a. 5 \(\frac{1}{3}\)

b. 5 \(\frac{2}{3}\)

c. 6 \(\frac{1}{3}\)

d. 11

Answer:

b. 5 \(\frac{2}{3}\)

Explanation:

Jose jumped 8 \(\frac{1}{3}\) feet. This was 2 \(\frac{2}{3}\) feet farther than Lila jumped.

8 \(\frac{1}{3}\) – 2 \(\frac{2}{3}\) = \(\frac{25}{3}\) – \(\frac{8}{3}\) = \(\frac{7}{3}\) = 5 \(\frac{2}{3}\)

### Page No. 557

Question 1.

Name the triangle. Tell whether each angle is acute, right, or obtuse.

A name for the triangle is __________ .

Name:

∠F is _________

∠G is _________

∠H is _________

Answer:

Right Triangle; Triangle FGH;

∠F and ∠H are acute angles.

∠G is Right angle

Explanation:

∠F and ∠H are acute angles with less than a right angle. ∠G is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

**Classify each triangle. Write acute, right, or obtuse.**

Question 2.

_____

Answer:

Obtuse triangle;

Angle B and Angle C are both acute.

Angle A is obtuse.

Explanation:

From triangle ABC, Angle B, and Angle C are both acute with less than a right angle. Angle A is obtuse angle that is greater than a right angle.

Question 3.

_____

Answer:

Obtuse triangle;

Angle A and Angle C are both acute.

Angle B is obtuse.

Explanation:

From triangle ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle. A triangle with an obtuse angle is called an obtuse triangle.

Question 4.

_____

Answer:

Acute triangle;

Angle A, Angle B, and Angle C are acute angles.

Explanation:

From triangle ABC, Angle A, Angle B, and Angle C are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle.

Question 5.

_____

Answer:

Right Triangle; Triangle ABC;

∠A and ∠C are acute angles.

∠B is Right angle

Explanation:

∠A and ∠C are acute angles with less than a right angle. ∠B is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Question 6.

_____

Answer:

Acute triangle;

Angle A, Angle B, and Angle C are acute angles.

Explanation:

From triangle ABC, Angle A, Angle B, and Angle C are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle.

Question 7.

_____

Answer:

Right Triangle;

∠A and ∠C are acute angles.

∠B is Right angle

Explanation:

∠A and ∠C are acute angles with less than a right angle. ∠B is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Question 8.

Cross out the figure that does not belong. Explain.

Type below:

_________

Answer:

Explanation:

From the given image, 1, 3, and 4 have two acute angles, and one obtuse angle. 2 have three acute angles.

### Page No. 558

**Use the Venn diagram for 9–10.**

Question 9.

Which triangles do NOT have an obtuse angle? Explain.

_______ triangles

Answer:

4 triangles;

Triangle DEF, Triangle SPN, Triangle ABC, and Triangle GHP are don’t have an obtuse angle. Triangle DEF, Triangle SPN are acute angles. An acute triangle is a triangle with three acute angles. Triangle ABC, and Triangle GHP are right angles. A right triangle is a triangle with one right angle. The sum of the triangle is 180 degrees. A right triangle has 90 degrees. So, the remaining angles must be acute angles.

Question 10.

How many triangles have at least two acute angles? Explain.

_______ triangles

Answer:

4 triangles;

Triangle DEF, Triangle SPN, Triangle ABC, and Triangle GHP at least two acute angles. Triangle DEF, Triangle SPN are acute angles. An acute triangle is a triangle with three acute angles. Triangle ABC, and Triangle GHP are right angles. A right triangle is a triangle with one right angle and two acute angles.

Question 11.

Use the square shown at the right. Draw a line segment from point M to point P. Name and classify the triangles formed by the line segment.

Type below:

_________

Answer:

Angle MNP and Angle MQP

Explanation:

The line segment from M to P forms Angle MNP and Angle MQP.

Question 12.

Write the letter of the triangle under its correct classification.

Type below:

_________

Answer:

Explanation:

Triangle A and triangle B have three acute angles. So, they are acute triangles. Triangle D and triangle F have one obtuse angle. So, they are obtuse triangles.

Triangle C and triangle E have one right angle. So, they are right triangles.

### Common Core – New – Page No. 559

**Classify Triangles**

**Classify each triangle. Write acute, right, or obtuse.**

Question 1.

Think: Angles A and C are both acute.

Angle B is obtuse.

Answer:

Obtuse triangle;

Angle A and Angle C are both acute.

Angle B is obtuse.

Explanation:

From triangle ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle.

Question 2.

_________

Answer:

Right Triangle; Triangle DEF;

∠D and ∠F are acute angles.

∠E is Right angle

Explanation:

∠D and ∠F are acute angles with less than a right angle. ∠E is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Question 3.

_________

Answer:

Acute triangle;

Angle G, Angle J, and Angle H are acute angles.

Explanation:

From triangle GJH, Angle G, Angle J, and Angle H are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle.

Question 4.

_________

Answer:

Obtuse triangle;

Angle L and Angle N are both acute.

Angle M is obtuse.

Explanation:

From triangle LMN, Angle L and Angle N are both acute with less than a right angle. Angle M is an obtuse angle that is greater than a right angle. A triangle with an obtuse angle is called an obtuse triangle.

**Problem Solving**

Question 5.

Use figure ABCD below. Draw a line segment from point B to point D. Name and classify the triangles formed.

Two _________ triangles

△ _________

△ _________

Answer:

Two Acute triangles.

△ ABD

△ BCD

Explanation:

If we draw a line segment from point B to point D, then there are two traingles formed with less than right angles. They are △ ABD and △ BCD.

Question 6.

Use figure ABCD below. Draw a line segment from point A to point C. Name and classify the triangles formed.

Two _________ triangles

△ _________

△ _________

Answer:

Two Acute triangles.

△ ABC

△ ADC

Explanation:

If we draw a line segment from point A to point C, then there are two traingles formed with less than right angles. They are △ ABC and △ ADC.

### Common Core – New – Page No. 560

**Lesson Check**

Question 1.

Stephen drew this triangle. How many obtuse angles does the triangle have?

Options:

a. 0

b. 1

c. 2

d. 3

Answer:

a. 0

Explanation:

The given image has three acute angles. So, there are 0 obtuse angles.

Question 2.

Joan was asked to draw a right triangle. How many right angles are in a right triangle?

Options:

a. 0

b. 1

c. 2

d. 3

Answer:

b. 1

Explanation:

A right triangle has only one right angle.

**Spiral Review**

Question 3.

Oliver drew the figure below to show light traveling from the sun to Earth. Name the figure he drew.

Options:

a. segment SE

b. ray SE

c. line SE

d. ray ES

Answer:

b. ray SE

Explanation:

SE is a ray that has one endpoint and continues without an end in one direction.

Question 4.

Armon added \(\frac{1}{10}\) and \(\frac{8}{100}\). Which is the correct sum?

Options:

a. \(\frac{18}{10}\)

b. \(\frac{9}{10}\)

c. \(\frac{9}{100}\)

d. \(\frac{18}{100}\)

Answer:

d. \(\frac{18}{100}\)

Explanation:

\(\frac{1 X 10}{10 X 10}\) + \(\frac{8}{100}\) = \(\frac{10}{100}\) + \(\frac{8}{100}\) = \(\frac{18}{100}\)

Question 5.

Sam counted out loud by 6s. Jorge counted out loud by 8s. What are the first three numbers both students said?

Options:

a. 8, 16, 24

b. 14, 28, 42

c. 24, 48, 72

d. 48, 96, 144

Answer:

c. 24, 48, 72

Explanation:

Sam counted out loud by 6s = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72.

Jorge counted out loud by 8s = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.

Both students said the first three numbers are 24, 48, 72.

Question 6.

A basketball team averaged 105 points per game. How many points did the team score in 6 games?

Options:

a. 605 points

b. 630 points

c. 900 points

d. 6,030 points

Answer:

b. 630 points

Explanation:

A basketball team averaged 105 points per game.

They score in 6 games = 6 x 105 = 630 points.

### Page No. 563

Question 1.

Draw and label \(\overline{Q R} \| \overline{S T}\).

Think: Parallel lines never intersect. Parallel line segments are parts of parallel lines.

Type below:

_________

Answer:

\(\overline{Q R} \| \overline{S T}\)

Explanation:

Parallel lines never intersect. Parallel line segments are parts of parallel lines.

**Use the figure for 2 and 3.**

Question 2.

Name two line segments that appear to be parallel.

Type below:

_________

Answer:

Line Segment CB and Line Segment DF.

Explanation:

Line Segment CB and Line Segment DF are parallel lines. The both lines never intersect and are always the same distance apart.

Question 3.

Name two line segments that appear to be perpendicular.

Type below:

_________

Answer:

Line Segment CB and Line Segment BF are perpendicular lines.

Explanation:

Line Segment CB and Line Segment DF are perpendicular lines. Both lines intersect to form four right angles.

**Use the figure for 4–5.**

Question 4.

Name a pair of lines that are perpendicular.

Type below:

_________

Answer:

FJ and HG are perpendicular lines.

Explanation:

FJ and HG lines intersect each other and form four right angles.

Question 5.

Name a pair of lines that appear to be parallel.

Type below:

_________

Answer:

DC and FJ are parallel lines.

Explanation:

DC and FJ are never intersected and are always the same distance apart.

Question 6.

\(\overline{R S} \| \overline{T U}\)

Type below:

_________

Answer:

\(\overline{R S} \| \overline{T U}\)

Explanation:

Parallel lines never intersect. Parallel line segments are parts of parallel lines.

Question 7.

\(\overrightarrow{K L} \text { and } \overrightarrow{K M}\)

Type below:

_________

Answer:

Explanation:

KL and KM are two rays and start at the same point K.

Question 8.

\(\overline{C D} \perp \overline{D E}\)

Type below:

_________

Answer:

\(\overline{C D} \perp \overline{D E}\)

Explanation:

\(\overline{C D} \perp \overline{D E}\) are two lines. They are intersect each other and form four right angles.

Question 9.

\(\overset { \longleftrightarrow }{ JK } \) ⊥ \(\overset { \longleftrightarrow }{ LM } \)

Type below:

_________

Answer:

\(\overset { \longleftrightarrow }{ JK } \) ⊥ \(\overset { \longleftrightarrow }{ LM } \)

Explanation:

JK and LM are two lines and intersected each other to form right angles.

Question 10.

\(\overset { \longleftrightarrow }{ ST } \) intersecting \(\overset { \longleftrightarrow }{ UV } \) at point X

Type below:

_________

Answer:

Explanation:

ST and UV are two lines intersecting at point X.

Question 11.

\(\overset { \longleftrightarrow }{ AB } \) || \(\overset { \longleftrightarrow }{ FG } \)

Type below:

_________

Answer:

\(\overset { \longleftrightarrow }{ AB } \) || \(\overset { \longleftrightarrow }{ FG } \)

Explanation:

Parallel lines never intersect. Parallel line segments are parts of parallel lines.

**Use the figure for 12–13.**

Question 12.

Dan says that \(\overset { \longleftrightarrow }{ HL } \) is parallel to \(\overset { \longleftrightarrow }{ IM } \). Is Dan correct? Explain.

_____

Answer:

No; HL and IM are not parallel lines. Parallel lines are always the same distance apart. But from the given image, the H and I may intersect if the line is extended.

Question 13.

Name two intersecting line segments that are not perpendicular.

Type below:

_________

Answer:

JM and KG are two intersecting line segments and also not perpendicular.

### Page No. 564

**Use the house plan at the right for 14–16.**

Question 14.

What geometric term describes a corner of the living room?

_________

Answer:

The corner of the living room is a vertex. Corners of any shape are vertexes.

Question 15.

Name three parts of the plan that show line segments.

_________

Answer:

Kitchen, Living Room, and Master Bedroom.

Question 16.

Name a pair of line segments that appear to be parallel

_________

Answer:

Two sidelines of Living Room are parallel.

Two sidelines of Master Bedroom are parallel.

**Use the map at the right for 17–19.**

Question 17.

Name a street that appears to be parallel to S 17^{th} Street.

_________

Answer:

S 18th Street

Explanation:

S 18th Street is parallel to S 17th Street. They never meet each other and are always the same distance apart.

Question 18.

Use Diagrams Name a street that appears to be parallel to Vernon Street.

_________

Answer:

Perry Street

Explanation:

Perry Street is parallel to Vernon Street. They never meet each other and are always the same distance apart.

Question 19.

Name a street that appears to be perpendicular to S 19^{th} Street.

_________

Answer:

Austin Street

Explanation:

Austin Street is perpendicular to S 19th Street. They are intersect with each other and form four right angles.

Question 20.

Choose the labels to make a true statement.

Type below:

_________

Answer:

Line AB is perpendicular to Line EF.

### Common Core – New – Page No. 565

**Parallel Lines and Perpendicular Lines**

**Use the figure for 1–3.**

Question 1.

Name a pair of lines that appear to be perpendicular.

Think: Perpendicular lines form right angles.

\(\overset { \longleftrightarrow }{ AB } \) and \(\overset { \longleftrightarrow }{ EF } \) appear to form right angles.

\(\overset { \longleftrightarrow }{ AB } \) and \(\overset { \longleftrightarrow }{ EF } \)

Answer:

\(\overset { \longleftrightarrow }{ AB } \) and \(\overset { \longleftrightarrow }{ EF } \)

Explanation:

Perpendicular lines form right angles.

\(\overset { \longleftrightarrow }{ AB } \) and \(\overset { \longleftrightarrow }{ EF } \) appear to form right angles.

\(\overset { \longleftrightarrow }{ AB } \) and \(\overset { \longleftrightarrow }{ EF } \)

Question 2.

Name a pair of lines that appear to be parallel.

_____ and _____

Answer:

\(\overset { \longleftrightarrow }{ AB } \) and \(\overset { \longleftrightarrow }{ CD} \)

Explanation:

Parallel lines never interest each other. \(\overset { \longleftrightarrow }{ AB } \) and \(\overset { \longleftrightarrow }{ CD} \) are parallel lines.

Question 3.

Name another pair of lines that appear to be perpendicular.

_____ and _____

Answer:

\(\overset { \longleftrightarrow }{ CD } \) and \(\overset { \longleftrightarrow }{ EF } \)

Explanation:

Perpendicular lines form right angles.

\(\overset { \longleftrightarrow }{ CD } \) and \(\overset { \longleftrightarrow }{ EF } \) appear to form right angles.

\(\overset { \longleftrightarrow }{ CD } \) and \(\overset { \longleftrightarrow }{ EF } \)

**Draw and label the figure described.**

Question 4.

\(\overset { \longleftrightarrow }{ MN } \) and \(\overset { \longleftrightarrow }{ PQ } \) intersecting at point R

Answer:

Explanation:

MN and PQ are two lines and interesting at point R.

Question 5.

\(\overset { \longleftrightarrow }{ WX } \) || \(\overset { \longleftrightarrow }{ YZ } \)

Answer:

Explanation:

WX and YZ are parallel lines and they never intersect with each other.

Question 6.

\(\overset { \longleftrightarrow }{ FH } \) ⊥ \(\overset { \longleftrightarrow }{ JK } \)

Answer:

Explanation:

FH and JK are two lines and intersecting each other to form four right angles.

**Problem Solving**

**Use the street map for 7–8.**

Question 7.

Name two streets that intersect but do not appear to be perpendicular.

Type below:

_________

Answer:

Maple and Oak or Oak and Birch

Explanation:

Maple and Oak or Oak and Birch; They are intersecting with each other and not perpendicular.

Question 8.

Name two streets that appear to be parallel to each other.

Type below:

_________

Answer:

Maple and Birch

Explanation:

Maple and Birch are streets and not intersect with each other. They appear to be parallel to each other.

### Common Core – New – Page No. 566

**Lesson Check**

Question 1.

Which capital letter appears to have perpendicular line segments?

Options:

a. N

b. O

c. T

d. V

Answer:

c. T

Explanation:

T has two lines and interesting to form four right angles.

Question 2.

In the figure, which pair of line segments appear to be parallel?

Options:

a. \(\overline{F G} \text { and } \overline{G H}\)

b. \(\overline{F J} \text { and } \overline{G H}\)

c. \(\overline{F G} \text { and } \overline{J H}\)

d. \(\overline{J H} \text { and } \overline{F J}\)

Answer:

c. \(\overline{F G} \text { and } \overline{J H}\)

Explanation:

\(\overline{F G} \text { and } \overline{J H}\) are parallel lines that never intersect

**Spiral Review**

Question 3.

Nolan drew a right triangle. How many acute angles did he draw?

Options:

a. 0

b. 1

c. 2

d. 3

Answer:

c. 2

Explanation:

A triangle with one right angle will have two acute angles.

Question 4.

Mike drank more than half the juice in his glass. What fraction of the juice could Mike have drunk?

Options:

a. \(\frac{1}{3}\)

b. \(\frac{2}{5}\)

c. \(\frac{3}{6}\)

d. \(\frac{5}{8}\)

Answer:

d. \(\frac{5}{8}\)

Explanation:

Mike drank more than half the juice in his glass. He drunk \(\frac{5}{8}\) of the juice.

Question 5.

A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. How many pencils were left?

Options:

a. 2

b. 4

c. 6

d. 142

Answer:

c. 6

Explanation:

A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. He shared 142 pencils for each of 7 teachers. So, 142 X 7 = 994. The remaining pencils are 6.

Question 6.

A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. How many ounces of juice did she buy?

Options:

a. 364 ounces

b. 370 ounces

c. 384 ounces

d. 402 ounces

Answer:

c. 384 ounces

Explanation:

A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. 64 X 6 = 384 ounces juice she can buy.

### Page No. 569

Question 1.

Tell whether the quadrilateral is also a trapezoid, parallelogram, rhombus, rectangle, or square.

Think:

____ pairs of parallel sides

____ sides of equal length

____ right angles

Quadrilateral ABCD is also a __________

__________

Answer:

2 pairs of parallel sides

4 sides of equal length

0 right angles.

Quadrilateral ABCD is also a Rhombus

Explanation:

A Rhombus is a quadrilateral that has 2 pairs of parallel sides and 4 sides of equal lengths.

**Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.**

Question 2.

__________

Answer:

Quadrilateral

Explanation:

0 pairs of parallel sides

0 sides of equal length

0 right angles.

The given image is quadrilateral.

The quadrilateral doesn’t have a name because it has 0 pairs of parallel sides, 0 sides of equal length, and 0 right angles.

Question 3.

_________

_________

_________

Answer:

Quadrilateral, Rectangle, and Parallelogram

Explanation:

2 pairs of parallel sides

2 pairs of sides of equal length

4 right angles.

Given quadrilateral is Rectangle and Parallelogram.

A Rectangle is a quadrilateral that has 2 pairs of parallel sides and 2 pairs of sides of equal lengths, and 4 right angles.

Question 4.

_________

_________

_________

Answer:

Quadrilateral, Parallelogram, and Rhombus

Explanation:

2 pairs of parallel sides

4 sides of equal length

0 right angles.

Given quadrilateral is Rhombus and Parallelogram.

A Rhombus is a quadrilateral that has 2 pairs of parallel sides and 4 sides of equal lengths, and 0 right angles.

Question 5.

_________

_________

Answer:

Quadrilateral and Parallelogram

Explanation:

2 pairs of parallel sides

2 pairs of sides of equal length

0 right angles.

Given quadrilateral is Parallelogram.

A Parallelogram is a quadrilateral that has 2 pairs of parallel sides and 2 pairs of sides of equal lengths, and 0 right angles.

Question 6.

_________

_________

_________

Answer:

Quadrilateral and Square

Explanation:

2 pairs of parallel sides

4 sides of equal length

4 right angles.

Given quadrilateral is Square.

A Square is a quadrilateral that has 2 pairs of parallel sides and 4 sides of equal lengths, and 4 right angles.

Question 7.

_________

_________

Answer:

Quadrilateral and Trapezoid

Explanation:

1 pair of parallel sides

0 sides of equal length

0 right angles.

Given quadrilateral is Trapezoid.

A Square is a quadrilateral that has 1 pair of parallel sides and 0 sides of equal lengths, and 0 right angles.

### Page No. 570

Question 8.

Explain how a rhombus and square are alike, and how they are different.

Type below:

_________

Answer:

The rhombus and square have 2 pairs of parallel sides and 4 sides of equal length. But the rhombus has 0 right angles and the square has 4 right angles.

Question 9.

Classify the figure. Select all that apply.

Options:

a. quadrilateral

b. trapezoid

c. parallelogram

d. rectangle

e. rhombus

f. square

Answer:

a. quadrilateral

b. trapezoid

c. parallelogram

Explanation:

A Parallelogram is a quadrilateral that has 2 pairs of parallel sides and 2 pairs of sides of equal lengths, and 0 right angles.

**The Louvre Museum is located in Paris, France. Architect I. M. Pei designed the glass and metal structure at the main entrance of the museum. This structure is called the Louvre Pyramid. Below is a diagram of part of the entrance to the Louvre Pyramid.**

Question 10.

Describe the quadrilaterals you see in the diagram.

_________

_________

Answer:

Trapezoid and Rhombus

Explanation:

There are 2 quadrilaterals available in the given image. One is Trapezoid with 1 pair of parallel sides. Another one is Rhombus is with 2 pairs of parallel sides and 4 sides of equal lengths, and 0 right angles.

Question 11.

How many triangles do you see in the diagram? Explain.

______ triangles

Answer:

11 triangles

Explanation:

The given image has 11 triangles

### Common Core – New – Page No. 571

**Classify Quadrilaterals**

**Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.**

Question 1.

Think: 2 pairs of parallel sides

4 sides of equal length

0 right angles

quadrilateral, parallelogram, rhombus

Answer:

Quadrilateral, Parallelogram, and rhombus.

Explanation:

2 pairs of parallel sides

4 sides of equal length

0 right angles

Quadrilateral, Parallelogram, and rhombus.

Question 2.

Type below:

_________

Answer:

Quadrilateral, Parallelogram, Rectangle

Explanation:

2 pairs of parallel sides

2 pairs of sides of equal length

4 right angles

Quadrilateral, Parallelogram, Rectangle

Question 3.

Type below:

_________

Answer:

Explanation:

1 pair of parallel sides

2 sides of equal length

0 right angles

Quadrilateral, Trapezoid

Question 4.

Type below:

_________

Answer:

Quadrilateral

Explanation:

0 pair of parallel sides

0 sides of equal length

0 right angles

Quadrilateral

Question 5.

Type below:

_________

Answer:

Quadrilateral, Parallelogram, and rhombus

Explanation:

2 pairs of parallel sides

4 sides of equal length

0 right angles

Quadrilateral, Parallelogram, and rhombus

Question 6.

Type below:

_________

Answer:

Explanation:

1 pair of parallel sides

0 sides of equal length

2 right angles

Quadrilateral, Trapezoid

Question 7.

Type below:

_________

Answer:

Explanation:

2 pairs of parallel sides

2 pairs of sides of equal length

0 right angles

Quadrilateral, Parallelogram

**Problem Solving**

Question 8.

Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. What figure did Alan draw

_________

Answer:

Quadrilateral or rhombus

Explanation:

Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. Alan drew Quadrilateral or rhombus

Question 9.

Teresa drew a quadrilateral with 2 pairs of parallel sides and 4 right angles. What quadrilateral could she have drawn?

_________

Answer:

square or rectangle

Explanation:

2 pairs of parallel sides and 4 right angles. she could draw a square or rectangle.

### Common Core – New – Page No. 572

**Lesson Check**

Question 1.

Joey is asked to name a quadrilateral that is also a rhombus. What should be his answer?

Options:

a. square

b. rectangle

c. parallelogram

d. trapezoid

Answer:

a. square

Explanation:

The quadrilateral square is also called a rhombus. Both square and rhombus have 2 pairs of parallel sides and 4 sides of equal length.

Question 2.

Which quadrilateral has exactly one pair of parallel sides?

Options:

a. square

b. rhombus

c. parallelogram

d. trapezoid

Answer:

d. trapezoid

Explanation:

A trapezoid has exactly one pair of parallel sides.

**Spiral Review**

Question 3.

Terrence has 24 eggs to divide into equal groups. What are all the possible numbers of eggs that Terence could put in each group?

Options:

a. 1, 2, 3, 4

b. 2, 4, 6, 8, 12

c. 1, 2, 3, 4, 6, 8, 12, 24

d. 24, 48, 72, 96

Answer:

c. 1, 2, 3, 4, 6, 8, 12, 24

Explanation:

Terrence has 24 eggs to divide into equal groups. Terence could put in each group in 1, 2, 3, 4, 6, 8, 12, 24 ways.

Question 4.

In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. What number

should Jenna say?

Options:

a. 31

b. 35

c. 39

d. 43

Answer:

b. 35

Explanation:

In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7.

7 + 4 = 11

11 + 4 = 15

15 + 4 = 19

19 + 4 = 23

23 + 4 = 27

27 + 4 = 31

31 + 4 = 35.

Jenna says 35.

Question 5.

Lou eats \(\frac{6}{8}\) of a pizza. What fraction of the pizza is left over?

Options:

a. \(\frac{1}{8}\)

b. \(\frac{1}{4}\)

c. \(\frac{1}{2}\)

d. \(\frac{3}{4}\)

Answer:

b. \(\frac{1}{4}\)

Explanation:

Lou eats \(\frac{6}{8}\) of a pizza. So, 6 parts of pizza is finished and remaining 2 parts of pizza is remained. So, the left over pizza is \(\frac{2}{8}\) = \(\frac{1}{4}\).

Question 6.

Which capital letter appears to have parallel lines?

Options:

a. D

b. L

c. N

d. T

Answer:

c. N

Explanation:

N has two parallel lines and never intersect each other.

### Page No. 573

**Choose the best term from the box to complete the sentence.**

Question 1.

A _______ is part of a line between two endpoints.

_________

Answer:

line segment

Question 2.

A _______ forms a square corner.

_________

Answer:

Right angle

Question 3.

An _______ is greater than a right angle and less than a straight angle.

_________

Answer:

Obtuse angle

Question 4.

The two-dimensional figure that has one endpoint is a ________.

_________

Answer:

ray

Question 5.

An angle that forms a line is called a _______.

_________

Answer:

straight line

Question 6.

On the grid below, draw a polygon that has 2 pairs of parallel sides, 2 pairs of sides equal in length, and 2 acute and 2 obtuse angles. Tell all the possible names for the figure.

Type below:

_________

Answer:

Parallelogram

Explanation:

The possible polygon that has 2 pairs of parallel sides, 2 pairs of sides equal in length, and 2 acute and 2 obtuse angles is Parallelogram.

**Draw the figure.**

Question 7.

parallel lines

Type below:

_________

Answer:

Explanation:

QR and ST are two parallel lines. they never intersect each other.

Question 8.

obtuse ∠ABC

Type below:

_________

Answer:

Explanation:

From triangle, ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle.

Question 9.

intersecting lines that are not perpendicular

Type below:

_________

Answer:

Explanation:

ST and UV are two lines intersecting at point X.

Question 10.

acute ∠RST

Type below:

_________

Answer:

### Page No. 574

Question 11.

Which triangle has one right angle?

_________

Answer:

A right triangle has one right angle.

Question 12.

Which figure has 2 pairs of parallel sides, 2 pairs of sides of equal length, and 4 right angles?

_________

Answer:

A Rectangle has 2 pairs of parallel sides, 2 pairs of sides of equal length, and 4 right angles.

Question 13.

Which quadrilateral can have 2 pairs of parallel sides, all sides with equal length, and no right angles?

_________

Answer:

Rhombus can have 2 pairs of parallel sides, all sides with equal length, and no right angles.

Question 14.

What is the correct name of the figure shown?

_________

Answer:

Ray

Explanation:

EF is a ray that has one endpoint and continues without an end in one direction.

Question 15.

Describe the angles of an obtuse triangle.

Type below:

_________

Answer:

An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles.

### Page No. 577

**Tell whether the parts on each side of the line match. Is the line a line of symmetry? Write yes or no.**

Question 1.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 2.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 3.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 4.

____

Answer:

No;

Explanation:

The line of symmetry divides a shape into two parts that are not with the same size and shape.

**Tell if the blue line appears to be a line of symmetry. Write yes or no.**

Question 5.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 6.

____

Answer:

No;

Explanation:

The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 7.

____

Answer:

No;

Explanation:

The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 8.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

**Tell if the blue line appears to be a line of symmetry. Write yes or no.**

Question 9.

____

Answer:

No;

The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 10.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 11.

____

Answer:

No;

The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 12.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 13.

Which best describes the symmetry in the letter I?

Type below:

________

Answer:

The two parts of the folded I match exactly. The fold line is a line of symmetry.

Explanation:

Take the Horizontal line in the middle of the Letter I. Cut out the tracing. Fold the tracing over a horizontal line. The two parts of the folded I match exactly. The fold line is a line of symmetry.

### Page No. 578

Question 14.

Which shape has a correctly drawn line of symmetry?

a. What do you need to find?

Type below:

________

Answer:

Find the shape that has an exact line of symmetry.

Question 14.

b. How can you tell if the line of symmetry is correct?

Type below:

________

Answer:

If the two parts of the folded match exactly, then the line is a line of symmetry.

Question 14.

c. Tell how you solved the problem.

Type below:

________

Answer:

From fig 1 to 4, the fig 2 is has a line of symmetry that can exactly separate the two parts equally.

Question 14.

d. Circle the correct shape above.

Type below:

________

Answer:

Question 15.

Reason Abstractly Draw a line of symmetry in the figure shown.

Answer:

Question 16.

Evie’s birthday is on the 18^{th} of May. Since May is the 5th month, Evie wrote the date as shown.

Evie says all the numbers she wrote have line symmetry. Is she correct? Explain.

Answer:

No; The number 5 doesn’t have a line of symmetry. So, Evie explanation is wrong.

### Common Core – New – Page No. 579

**Line Symmetry**

**Tell if the dashed line appears to be a line of symmetry. Write yes or no.**

Question 1.

yes

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 2.

____

Answer:

No;

The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 3.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 4.

____

Answer:

No;

The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 5.

____

Answer:

No;

The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 6.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

Question 7.

____

Answer:

No;

The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 8.

____

Answer:

Yes;

Explanation:

The line of symmetry divides a shape into two parts that are the same size and shape.

**Complete the design by reflecting over the line of symmetry.**

Question 9.

Answer:

Question 10.

Answer:

*Problem Solving*

Question 11.

Kara uses the pattern below to make paper dolls. The dashed line represents a line of symmetry. A complete doll includes the reflection of the pattern over the line of symmetry. Complete the design to show what one of Kara’s paper dolls looks like.

Answer:

### Common Core – New – Page No. 580

**Lesson Check**

Question 1.

Which best describes the line of symmetry in the letter D?

Options:

a. horizontal

b. vertical

c. diagonal

d. half turn

Answer:

a. horizontal

Explanation:

The horizontal line of symmetry in the letter D can exactly separate two parts equally.

Question 2.

Which shape has a correctly drawn line of symmetry?

Options:

a.

b.

c.

d.

Answer:

b.

Explanation:

Image b has the line of symmetry that separates two parts equally.

**Spiral Review**

Question 3.

The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. How many unit cubes will each group get?

Options:

a. 40

b. 44

c. 45

d. 48

Answer:

c. 45

Explanation:

The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. 360/8= 45.

Question 4.

There are 5,280 feet in one mile. How many feet are there in 6 miles?

Options:

a. 30,680

b. 31,260

c. 31,608

d. 31,680

Answer:

d. 31,680

Explanation:

There are 5,280 feet in one mile. So, for 6 miles = 6 x 5, 280 = 31,680.

Question 5.

Sue has 4 pieces of wood. The lengths of her pieces of wood are \(\frac{1}{3}\) foot, \(\frac{2}{5}\) foot, \(\frac{3}{10}\) foot, and \(\frac{1}{4}\) foot. Which piece of wood is the shortest?

Options:

a. the \(\frac{1}{3}\) foot piece

b. the \(\frac{2}{5}\) foot piece

c. the \(\frac{3}{10}\) foot piece

d. the \(\frac{1}{4}\) foot piece

Answer:

d. the \(\frac{1}{4}\) foot piece

Explanation:

The lengths of \(\frac{1}{4}\) foot piece is less compared to other lengths.

Question 6.

Alice has \(\frac{1}{5}\) as many miniature cars as Sylvester has. Sylvester has 35 miniature cars. How many miniature cars does Alice have?

Options:

a. 7

b. 9

c. 40

d. 175

Answer:

a. 7

Explanation:

Alice has \(\frac{1}{5}\) as many miniature cars as Sylvester has. Sylvester has 35 miniature cars. Alice have \(\frac{1}{5}\) X 35 = 7 miniature cars.

### Page No. 583

Question 1.

The shape at the right has line symmetry. Draw the 2 lines of symmetry.

Type below:

_________

Answer:

**Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1.**

Question 2.

_________

Answer:

more than 1

Explanation:

There is more than 1 line of symmetries that separates two parts equally.

Question 3.

_________

Answer:

more than 1

Explanation:

There is more than 1 lines of symmetries that separates two parts equally.

Question 4.

_________

Answer:

1 line

Explanation:

There is 1 line of symmetry that separates two parts equally.

Question 5.

_________

Answer:

zero lines

Explanation:

There is no line of symmetries that separates two parts equally.

**Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1.**

Question 6.

_________

Answer:

more than 1

Explanation:

There is more than 1 lines of symmetries that separate two parts equally.

Question 7.

_________

Answer:

zero lines

Explanation:

There is no line of symmetries that separates two parts equally.

Question 8.

_________

Answer:

zero lines

Explanation:

There is no line of symmetries that separates two parts equally.

Question 9.

_________

Answer:

1 line

Explanation:

There is 1 line of symmetry that separates two parts equally.

**Practice: Copy and Solve Does the design have line symmetry?**

**Write yes or no. If your answer is yes, draw all lines of symmetry.**

Question 10.

____

Answer:

Yes;

Question 11.

_____

Answer:

No;

Question 12.

_____

Answer:

Yes;

Question 13.

_____

Answer:

No;

Question 14.

Draw a figure that has 5 sides and exactly 1 line of symmetry.

Type below:

_________

Answer:

Explanation:

the above 5 sides shape has only 1 line symmetry

### Page No. 584

**Use the chart for 15–17.**

Question 15.

Which letters appear to have only 1 line of symmetry?

Type below:

_________

Answer:

A, B, C, D, E, T, U, V, W

Explanation:

The letters A, B, C, D, E, T, U, V, W have only 1 line of symmetry.

Question 16.

Which letters appear to have zero lines of symmetry?

Type below:

_________

Answer:

J, N, S

Explanation:

The letters J, N, S have only zero lines of symmetry.

Question 17.

The letter C has horizontal symmetry. The letter A has vertical symmetry. Which letters appear to have both horizontal and vertical symmetry?

Type below:

_________

Answer:

H and I

Explanation:

The letters H and I have both horizontal and vertical symmetry.

Question 18.

Verify the Reasoning of Others Jeff says that the shape has only 2 lines of symmetry.

Does his statement make sense? Explain.

Type below:

_________

Answer:

No; Jeff’s explanation is wrong. Because the given shape has only 2 lines of symmetry.

Question 19.

Match each figure with the correct number of lines of symmetry it has.

Type below:

_________

Answer:

### Common Core – New – Page No. 585

**Find and Draw Lines of Symmetry**

**Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1.**

Question 1.

1

Answer:

more than 1

Explanation:

There is more than 1 line of symmetry that separates two parts equally.

Question 2.

________

Answer:

more than 1

Explanation:

There is more than 1 line of symmetry that separates two parts equally.

Question 3.

________

Answer:

Zero

Explanation:

There are 0 lines of symmetries.

Question 4.

________

Answer:

more than 1

Explanation:

There is more than 1 line of symmetry that separates two parts equally.

**Does the design have line symmetry? Write yes or no.**

**If your answer is yes, draw all lines of symmetry.**

Question 5.

_____

Answer:

Yes;

Question 6.

_____

Answer:

Yes;

_____

Answer:

No;

Question 8.

______

Answer:

Yes;

**Draw a shape for the statement. Draw the line or lines of symmetry.**

Question 9.

zero lines of symmetry

Answer:

Question 10.

1 line of symmetry

Answer:

Question 11.

2 lines of symmetry

Answer:

**Problem Solving**

**Use the chart for 12–13.**

Question 12.

Which number or numbers appear to have only 1 line of symmetry?

_____

Answer:

3

Explanation:

The number 3 has only 1 line of symmetry.

Question 13.

Which number or numbers appear to have 2 lines of symmetry?

_____

Answer:

0 and 8

Explanation:

The numbers 0 and 8 appear to have 2 lines of symmetry.

### Common Core – New – Page No. 586

**Lesson Check**

Question 1.

How many lines of symmetry does this shape appear to have?

Options:

a. 0

b. 2

c. 6

d. 12

Answer:

c. 6

Explanation:

The given shape has 6 lines of symmetries.

Question 2.

Which of the following shapes appears to have exactly 1 line of symmetry?

Options:

a.

b.

c.

d.

Answer:

d.

Explanation:

The trapezoid has exactly 1 line of symmetry.

**Spiral Review**

Question 3.

Richard practiced each of 3 piano solos for \(\frac{5}{12}\) hour. How long did he practice in all?

Options:

a. \(\frac{2}{3}\) hours

b. 1 \(\frac{1}{4}\) hours

c. 1 \(\frac{1}{3}\) hours

d. 1 \(\frac{5}{12}\) hours

Answer:

b. 1 \(\frac{1}{4}\) hours

Explanation:

Richard practiced each of 3 piano solos for \(\frac{5}{12}\) hour. \(\frac{5}{12}\) hour = 1 \(\frac{1}{4}\) hours hours.

Question 4.

Which of the following decimals is equivalent to three and ten hundredths?

Options:

a. 0.30

b. 0.31

c. 3.01

d. 3.1

Answer:

d. 3.1

Explanation:

three and ten hundredths = 310 hundredths = 3.1

Question 5.

Lynne used \(\frac{3}{8}\) cup of flour and \(\frac{1}{3}\) cup of sugar in a recipe. Which number below is a common denominator for \(\frac{3}{8}\) and \(\frac{1}{3}\)?

Options:

a. 8

b. 12

c. 16

d. 24

Answer:

d. 24

Explanation:

Lynne used \(\frac{3}{8}\) cup of flour and \(\frac{1}{3}\) cup of sugar in a recipe. To find the common denominator for \(\frac{3}{8}\) and \(\frac{1}{3}\), multiply 8 X3 and 3 X 8 = 24.

Question 6.

Kevin draws a figure that has four sides. All sides have the same length. His figure has no right angles. What figure does Kevin draw?

Options:

a. square

b. trapezoid

c. rhombus

d. rectangle

Answer:

c. rhombus

Explanation:

### Page No. 589

Question 1.

Marisol is making a pattern with blocks. What might the missing shape be?

First, look at the blocks.

Next, describe the pattern.

Type below:

_________

Answer:

The first image 1 has three line segments. The next shape will have four line segments.

Question 1.

Finally, draw the missing shape.

Type below:

_________

Answer:

Question 2.

Use the shapes to write a number pattern. Then describe the pattern in the numbers.

Answer:

Shape 1: Triangle

Shape 2: Square

Shape 3: Pentagon

Shape 4: Hexagon

Shape 5: Heptagon

Question 3.

What if the pattern continued? Write an expression to describe the number of sides the sixth shape has in Marisol’s pattern.

Type below:

_________

Answer:

If the pattern continued, then the next shape will have one more extra line segment to it. The sixth shape will become the octagon.

Shape 6: Octagon

Question 4.

Sahil made a pattern using circles. The first nine circles are shown. Describe the pattern. If Sahil continues the pattern, what might the next three circles be?

Type below:

_________

Answer:

The pattern is repeated for every three circles. One big circle followed by two small circles.

### Page No. 590

**Use the toy quilt designs for 5–6.**

Question 5.

Lu is making a quilt that is 20 squares wide and has 24 rows. The border of the quilt is made by using each toy design equally as often. Each square can hold one design. How many of each design does she use for the border?

______ times

Answer:

The border will have 20 squares two times, and 24 squares two times as well, that is the perimeter or the border, because a quilt has 4 sides:

20 X 2 + 24 X 2 = 40 + 48 = 88

So, the border will have 88 squares in total. So if the border can have only one design, Lu can use any toy design 88 times if she wants the border to have the same toy design in it.

Question 6.

Communicate Starting in the first square of her quilt, Lu lined up her toy designs in this order: plane, car, fire truck, helicopter, crane, and wagon. Using this pattern unit, which design will Lu place in the fifteenth square? Explain how you found your answer.

_________

Answer:

The answer is fire truck. As the pattern repeats, the fifteenth square will fire truck.

Question 7.

Missy uses 1 hexagonal, 2 rectangular, and 4 triangular pieces of fabric to make 1 bug design for a quilt. If she uses 70 pieces in all to make bug designs, how many of each shape does she use?

Hexagonal: _________ shapes

Rectangular: _________ shapes

Triangular: _________ shapes

Answer:

Hexagonal: 10 shapes

Rectangular: 10 shapes

Triangular: 10 shapes

(1 x 10) + (2 x 10) + (4 x 10) = 10 + 20 + 40 = 70 pieces in all.

Question 8.

Norris drew the pattern shown.

Label the circles to show the colors in the fourth figure of the pattern.

Type below:

_________

Answer:

### Common Core – New – Page No. 591

**Problem Solving Shape Patterns**

**Solve each Problem.**

Question 1.

Marta is using this pattern to decorate a picture frame. Describe the pattern. Draw what might be the next three figures in the pattern.

Possible answer: the pattern repeats: one trangle followed by two squares.

Answer:

The pattern repeats one triangle followed by two squares.

Question 2.

Describe the pattern. Draw what might be the next three figures in the pattern. How many circles are in the sixth figure in the pattern?

_____ circles

Answer:

Add one more column with 1 more circle than in the previous column; 21.

Question 3.

Larry stencils this pattern to make a border at the top of his bedroom walls. Describe the pattern. Draw what might be the missing figure in the pattern.

Answer:

2 triangles placed side to side followed by 2 sets of 2 triangles placed vertex to vertex

### Common Core – New – Page No. 592

**Lesson Check**

Question 1.

What might be the next three figures in this pattern?

Options:

a.

b.

c.

d.

Answer:

a.

Explanation:

the pattern has odd numbers of up arrows then even number of down arrows. So, the next three figures are .

Question 2.

Which might be the missing figure in the following pattern?

Options:

a.

b.

c.

d.

Answer:

**a. **

Explanation:

From the pattern, the missing image will have vertical rectangle with the circle and X mark in it.

**Spiral Review**

Question 3.

Chad has two pieces of wood. One piece is \(\frac{7}{12}\) foot long. The second piece is \(\frac{5}{12}\) foot longer than the first piece. How long is the second piece?

Options:

a. \(\frac{2}{12}\) foot

b. \(\frac{1}{2}\) foot

c. \(\frac{12}{18}\) foot

d. 1 foot

Answer:

d. 1 foot

Explanation:

\(\frac{7}{12}\) + \(\frac{5}{12}\) = \(\frac{12}{12}\) = 1 foot.

Question 4.

Olivia finished a race in 40.64 seconds. Patty finished the race in 40.39 seconds. Miguel finished the race in 41.44 seconds. Chad finished the race in 40.46 seconds. Who finished the race in the least time?

Options:

a. Olivia

b. Patty

c. Miguel

d. Chad

Answer:

b. Patty

Explanation:

Patty finished the race in 40.39 seconds that is the least time compared to others.

Question 5.

Justin bought 6 ribbons for an art project. Each ribbon is \(\frac{1}{4}\) yard long. How many yards of ribbon did Justin buy?

Options:

a. \(\frac{2}{3}\) yard

b. 1 \(\frac{1}{4}\) yards

c. 1 \(\frac{1}{2}\) yards

d. 1 \(\frac{3}{4}\) yards

Answer:

c. 1 \(\frac{1}{2}\) yards

Explanation:

Justin bought 6 ribbons for an art project. Each ribbon is \(\frac{1}{4}\) yard long. So, 6 X \(\frac{1}{4}\) = \(\frac{3}{2}\) = 1 \(\frac{1}{2}\) yards.

Question 6.

Kyle and Andrea were asked to make a list of prime numbers.

Kyle: 1, 3, 7, 19, 23

Andrea: 2, 3, 5, 7, 11

Whose list is correct?

Options:

a. Only Kyle’s list

b. Only Andrea’s list

c. Both lists are correct.

d. Neither list is correct.

Answer:

b. Only Andrea’s list

Explanation:

1 is not a prime number. So, the answer is Only Andrea’s list is correct.

### Page No. 593

Question 1.

Gavin is designing a kite. He sketched a picture of the kite.

How many right angles does the kite appear to have?

_____ right angles

Answer:

0 right angles

Explanation:

There is no right angles in the given shape.

Question 2.

Write the letter of the triangle under its correct classification.

Answer:

Explanation:

C and F are Acute angles with less than right angles.

B and D are Obtuse Angles with more than right angles.

A and E are Right Angles.

Question 3.

Select the angles that identify an obtuse triangle. Mark all that apply.

Options:

a. acute, acute, acute

b. acute, acute, obtuse

c. right, acute, acute

d. obtuse, right, acute

Answer:

b. acute, acute, obtuse

Explanation:

An obtuse triangle will have one obtuse angle and two acute angles.

### Page No. 594

Question 4.

Write the word that describes the part of Figure A written below.

\(\overline{E B}\) _________

\(\overset { \longleftrightarrow }{ AB } \) _________

\(\overrightarrow{G A}\) _________

∠EBG _________

∠CGB _________

Answer:

\(\overline{E B}\) line segment.

\(\overset { \longleftrightarrow }{ AB } \) Line.

\(\overrightarrow{G A}\) Ray.

∠EBG right angle.

∠CGB acute angle.

Explanation:

\(\overline{E B}\) is a line segment that has two endpoints connected to form a line.

\(\overset { \longleftrightarrow }{ AB } \) is a Line that continues without an end in both directions.

\(\overrightarrow{G A}\) is a Ray that has one endpoint and continues without an end in one direction.

∠EBG right angle.

∠CGB is an acute angle with less than the right angle.

Question 5.

What term best describes the figure shown below?

Answer:

perpendicular lines

Explanation:

The lines are forming four right angles they form squares. So, the both lines are perpendicular lines.

Question 6.

Naomi leaves for her trip to Los Angeles on the 12th day of August. Since August is the 8th month, Naomi wrote the date as shown.

Naomi says all the numbers she wrote have line symmetry. Is she correct? Explain your thinking.

_______

Answer:

Naomi is incorrect. The number 2 does not have a line of symmetry because if it were cut out, there would be no way to fold it in half so that the two parts matched exactly.

### Page No. 595

Question 7.

Max made a pennant that looks like a triangle. How can you classify the triangle based upon its angles?

The triangle is a(n) ____________ triangle.

Answer:

The triangle is an acute triangle.

Explanation:

The triangle is an acute triangle. because it has angles with less than right angles.

Question 8.

Choose the labels to make a true statement.

_____ is parallel to ______

Answer:

Line AB is parallel to line CD.

Explanation:

From the given image, Line AB is parallel to line CD.

Question 9.

Classify the figure. Select all that apply.

Options:

a. quadrilateral

b. trapezoid

c. parallelogram

d. rectangle

e. rhombus

f. square

Answer:

a. quadrilateral

b. trapezoid

c. parallelogram

d. rectangle

Explanation:

The given image has 2 parallel sides, 2 pairs of sides of length, and four right angles. So, the possible answers are quadrilateral, trapezoid, parallelogram, and rectangle.

Question 10.

Lily designed a deck in her backyard that looks like a quadrilateral that has only 1 pair of parallel sides. How can you classify the figure?

The quadrilateral is a ________

Answer:

The quadrilateral is a trapezoid

Explanation:

Lily designed a deck in her backyard that looks like a quadrilateral that has only 1 pair of parallel sides. So, the answer is a trapezoid.

### Page No. 596

Question 11.

Match each figure with the correct number of lines of symmetry it has.

Answer:

Explanation:

Image 1: 1 line of symmetry

Image 2: 2 lines of symmetry

Image 3: 0 lines of symmetry

Image 4: More than 2 lines of symmetry.

Question 12.

Barb drew the pattern shown.

Use the square shown to draw the missing pattern. □

Answer:

Explanation:

The fourth shape must consist of one extra square box in the top line and bottom line.

Question 13.

Claudia drew the figure below. Draw a line of symmetry on Claudia’s figure.

Answer:

Explanation:

The image can have one line symmetry.

Question 14.

Write the word or words that best describe this figure.

_________

Answer:

Ray

Explanation:

The ray that has one endpoint and continues without an end in one direction.

Question 15.

How many acute angles does a right triangle have?

A right triangle has ____ acute angles.

Answer:

A right triangle has 2 acute angles.

### Page No. 597

Question 16.

Mike drew a figure with opposite sides parallel. Write the pairs of parallel sides. What figure is it?

Answer:

Line DG is parallel to Line FE and Line DE is parallel to Line GF; the figure is a parallelogram.

Question 17.

Circle the letter that does not have line symmetry.

Answer:

Explanation:

The S does not have line symmetry.

Question 18.

Joseph made a pattern using ovals and rectangles. The first four figures of his pattern are shown. Draw the next figure in the pattern.

Answer:

Question 19.

Jeremy drew Figure 1 and Louisa drew Figure 2.

Part A

Jeremy says both figures are rectangles. Do you agree with Jeremy?

Support your answer.

_____

Answer:

Yes; both figures have 2 pairs of parallel sides, opposite sides that are equal in length, and 4 right angles.

Question 19.

Part B

Louisa says both figures are rhombuses. Do you agree with Louisa?

Support your answer.

_____

Answer:

No; figure 2 is a rhombus since it has 2 pairs of parallel sides and 4 sides of equal length. Figure 1 does not have 4 sides of equal length so it cannot be a rhombus.

### Page No. 598

Question 20.

Veronica found the number of lines of symmetry for the figure below. How many lines of symmetry does it have?

______ lines of symmetry

Answer:

2 lines of symmetry

Explanation:

the given shape can have 2 lines of symmetry.

Question 21.

Jordan drew the pattern below.

Part A

Describe the pattern.

Answer:

Each figure has 2 more squares than the preceding figure.

Question 21.

Part B

Write a rule using numbers to find the number of squares in any figure in the pattern.

Answer:

multiply the figure number by 2.

Question 21.

Part C

Draw Figure 5.

Answer:

### Page No. 603

Tell what fraction of the circle the shaded angle represents.

Question 1.

\(\frac{□}{□}\)

Answer:

\(\frac{1}{2}\)

Explanation:

Half of the part is shaded out of the circle. So, the answer is 1/2.

Question 2.

\(\frac{□}{□}\)

Answer:

\(\frac{1}{4}\)

Explanation:

\(\frac{1}{4}\) part of the circle is shaded out of the circle.

Question 3.

\(\frac{□}{□}\)

Answer:

\(\frac{3}{4}\)

Explanation:

3 parts of the circle is shaded out of the circle

Question 4.

\(\frac{□}{□}\)

Answer:

\(\frac{1}{1}\) = 1

Explanation:

The complete circle is shaded. So, the answer is 1.

Question 5.

\(\frac{□}{□}\)

Answer:

\(\frac{1}{2}\)

Explanation:

Half of the part is shaded out of the circle. So, the answer is 1/2.

Question 6.

\(\frac{□}{□}\)

Answer:

\(\frac{1}{12}\)

**Tell whether the angle on the circle shows a \(\frac{1}{4}, \frac{1}{2}, \frac{3}{4}\), or 1 full turn clockwise or counterclockwise.**

Question 7.

Type below:

________

Answer:

\(\frac{3}{4}\); counterclockwise

Explanation:

The image shows the counterclockwise and formed the fraction of \(\frac{3}{4}\).

Question 8.

Type below:

________

Answer:

\(\frac{1}{2}\); clockwise

Explanation:

The image shows the clockwise and formed the fraction of \(\frac{1}{2}\).

Question 9.

Type below:

________

Answer:

\(\frac{1}{4}\); clockwise

Explanation:

The image shows the clockwise and formed the fraction of \(\frac{1}{4}\).

Question 10.

Susan watched the game from 1 p.m. to 1:30 p.m. Describe the turn the minute hand made.

Type below:

________

Answer:

The minute hand made a \(\frac{1}{2}\) turn clockwise.

Question 11.

Compare the angles in Exercises 1 and 5. Does the position of the angle affect the size of the angle? Explain.

_____

Answer:

No; The size of the angle does not depend on the lengths of its sides.

### Page No. 604

Question 12.

Malcolm drew this angle on the circle. Which of the following describes the angle? Mark all that apply.

Options:

a. \(\frac{3}{4}\) turn

b. \(\frac{1}{4}\) turn

c. clockwise

d. counterclockwise

Answer:

a. \(\frac{3}{4}\) turn

d. counterclockwise

Explanation:

The image show the \(\frac{3}{4}\) turn and also the counterclockwise.

**Sense or Nonsense?**

Question 13.

Whose statement makes sense? Whose statement is nonsense? Explain your reasoning.

Type below:

__________

Answer:

The girl’s statement makes sense. The boy’s statement makes non-sense. Because from the figure it is clearly shown that the shaded part is \(\frac{1}{4}\) of the circle. There is no particular direction given to measure the shaded part.

### Conclusion:

Finally, you will find detailed solutions to all questions that you’re looking for. So, you can attempt the exam with utmost confidence and secure good grades in the exams. The topics covered in Ch 10 Two-dimensional figures are such Lines, Rays, Angles, Classify Triangles by Angles, Parallel Lines and Perpendicular Lines, etc. Understand how to solve the problems of two-dimensional figures by accessing our **Go Math Grade 4 Solution Key Chapter 10 Two-dimensional figures Homework Practice FL.**