Identify and Describe Geometric Figures

CHAPTE R

10

Identify and Describe Geometric Figures

connectED.mcgraw-hill.com co onn

The

BIG Idea

Investigate

How can I identify and describe two- and three-dimensional figures and angles?

Animations Vocabulary Math Songs Multilingual eGlossary

Learn Personal Tutor Virtual Manipulatives Audio

Make this Foldable to help organize information about geometric figures and angles. Begin with 4 sheets of notebook paper.

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Ident ify and Descr ib Geom e etric Figure s

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3 4 5 1-6

Foldables

New Vocabulary

Practice Self-Check Practice eGames

angle ángulo a figure that is formed by two rays with the same endpoint

Worksheets

Key Vocabulary

Assessment

English two-dimensional figure polygon three-dimensional figure vertex

492

Español figura plana polígono figura sólida vértice

When Will I Use This? Andrew and Teresa inTricky Turns Hey, Teresa, did you see that?

No, what did I miss?

I just did a 360!

Wow, do it again! I want to see!

I’ve never seen that trick.

Oww! Yeah, I just invented it. It’s the 360 Splat!

Look, I’ll try it again.

Well, that’s really cool, but I don’t think that’s a 360. Everyone’s a critic!

Your Tthuisrn! You will sollve err. teer problem in the chap


493

Are You Ready

for the Chapter?

Text Option

You have two options for checking Prerequisite Skills for this chapter.

Take the Quick Check below.

How many sides does each figure have? 1.

2.

3.

4. The musical instrument at the right resembles a triangle. How many sides does the instrument have?

Identify each figure. 7.

8. Identify the three-dimensional figure that represents the objects at the right.

5

6

Identify each figure. 9.

10.

Online Option 494 4

11.

Take the Online Readiness Quiz.


7

6.

14 5

5.

Multi-Part Lesson

1

Two- and Three-Dimensional Figures

PART

A

Main Idea I will identify, describe, and classify twodimensional figures.

Vocabulary V ttwo-dimensional figure polygon sides triangle quadrilateral pentagon

B

C

Two-Dimensional Figures A two-dimensional figure is a plane figure. It has length and width. Polygons are closed plane figures that have three or more line segments, called sides , and angles. The shapes of the signs are two-dimensional figures.

hexagon octagon decagon

Polygons

circle center radius diameter

Get ConnectED GLE 0406.4.1 Understand and use the properties of lines, segments, angles, polygons, and circles. Also addresses GLE 0406.1.1, SPI 0406.4.5.

A triangle has 3 sides and 3 angles.

A quadrilateral has 4 sides and 4 angles.

A pentagon has 5 sides and 5 angles.

A hexagon has 6 sides and 6 angles.

An octagon has 8 sides and 8 angles.

A decagon has 10 sides and 10 angles.

Identify a Polygon SPORTS Identify the shape of home plate. Look at the shape of the home plate. It has 5 sides and 5 angles. So, this figure is a pentagon.

Lesson 1A Two- and Three-Dimensional Figures 495

A circle is not a polygon because it does not have straight sides. Other figures are not polygons as well. Polygons

Not Polygons

Polygons have straight sides only, not curved sides.

Identify a Polygon Tell whether each figure is a polygon.

The figure has curved sides. It is not a polygon.

The figure has 6 straight sides. It is a polygon.

Identify d if each polygon. See Example 1 1.

2.

3.

Tell whether each figure is a polygon. See Examples 2 and 3 4.

5.

7. Identify the shape of the nut.

496


6.

8.

E

TALK MATH If we take a quadrilateral

and cut it into two pieces, what shapes could the pieces be?

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Identify each polygon. polygon See Example 1 9.

10.

11.

12.

13.

14.

Tell whether each figure is a polygon. See Examples 2 and 3 15.

16.

17.

18.

19.

20.

Identify the polygons that compose each figure. 21.

22.

23. OPEN ENDED Draw and identify a polygon. 24. WHICH ONE DOESN’T BELONG? Identify the figure that does not belong with the other three. Explain.

25.

E

WRITE MATH Explain how a hexagon and an octagon are the same. How are they different? Lesson 1A Two- and Three-Dimensional Figures 497

Two-Dimensional Figures A circle is a two-dimensional closed figure in which all points are the same distance from a fixed point, called the center . The parts of a circle are below.

Parts of a Circle

A line segment that connects the center of a circle to a point on the circle is a radius of the circle.

F

G

Line segment FG is the radius. A line segment that connects two points on a circle and goes through the center of a circle is a diameter of a circle.

C

D

Line segment CD is the diameter.

Identify the given points or line segments for each circle. 26. line segment JK

27. line segment LN

28. point V T

H

J

K

L

M

N

U

V

W

Sports

Disc golf was invented in the 1960s. Different weight discs are used for throwing various distances. A small diameter disc is used as a place marker.

4 in. 4 in.

Disc A

29. What is the radius of disc A? 30. What is the diameter of disc B? 31. Which disc is used as a place marker?

498


Disc B

Multi-Part Lesson

1


PART

A

Main Idea I will identify and describe threedimensional figures and identify and draw nets.

B

C

D

E

Three-Dimensional Figures A three-dimensional figure is a solid figure. It has length, width, and height.

Vocabulary V three-dimensional t figure face edge vertex

• A face is a flat side.

face

vertex

• Two faces meet at an edge . • A vertex is where three or more faces meet.

edge

net

Get ConnectED GLE 0406.4.1 Understand and use the properties of lines, segments, angles, polygons, and circles. Also addresses SPI 0406.4.5.

Three-Dimensional Figures

rectangular prism

triangular prism

square pyramid

cone

triangular pyramid

sphere

cube

cylinder

Identify ThreeDimensional Objects GIFTS Tell the number of faces, edges, and vertices. Then identify y the shape of the gift box. It has 6 faces, 12 edges, and 8 vertices. tice es. The gift box is a rectangular prism.

Lesson 1B Two- and Three-Dimensional Figures

499

A net is a two-dimensional figure that can be folded to make a three-dimensional figure.

Mini-Activity

Look at the shape of each face on a net to determine the threedimensional figure it

Step 1

Using grid paper, draw and cut out the net shown.

Step 2

Fold along the dotted lines. Tape the edges.

Step 3

Identify the threedimensional figure.

will make.

1. Draw another net that could be used to form a cube. 2. Identify the three-dimensional figure the net shown at the right makes. 3. Explain how to identify a three-dimensional figure from its net without folding the paper.

Tell ll the h number of faces, edges, and vertices. Then identify each figure. See Example 1 1.

2.

3.

Identify the three-dimensional figure each net makes. 4.

5.

7. Name two three-dimensional figures that have at least 1 circular face. 500 5


6.

8.

E

TALK MATH Compare a triangular

prism and a triangular pyramid.

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Tell edges, and Then id identify T ll the th number b off faces, f d d vertices. ti Th tif each figure. See Example 1

9.

10.

11.

12.

13.

14.

Identify the three-dimensional figure each net makes. 15.

16.

18.

17.

19.

20.

21. This three-dimensional figure has 4 faces, 6 edges, and 4 vertices. What figure is it?

22. This three-dimensional figure can be made using 2 circles and 1 large rectangle. What figure is it?

23. OPEN ENDED Draw a three-dimensional figure composed of 2 or more solids. Then describe its faces, edges, and vertices. 24. WHICH ONE DOESN’T BELONG? Identify the figure that does not belong with the other three. Explain.

25.

E

WRITE MATH Compare a cone and a cylinder. Lesson 1B Two- and Three-Dimensional Figures

501

Multi-Part Lesson

1


PART

A

B

C

Problem-Solving Strategy:

Look for a Pattern

Main Idea I will solve problems by looking for a pattern. Amado is helping his dad put tile on a table top. They are laying the tiles in a pattern. They have run out of tiles and need to buy more. What color of tiles need to be purchased to complete the table?

Understand

What facts do you know?

• You know the tiles form a pattern. • You know they need to buy more tiles. What do you need to find? • Find the tile colors that need to be purchased.

Plan

Look for a pattern. Then continue the pattern to find the missing tiles.

Solve

There are two rows of tile, and the tiles repeat red, green, blue, and yellow.

In the first row, the missing tiles are blue and green. In the second row, the missing tiles are red, blue, and yellow. So, Amado and his father need 2 blue, 1 green, 1 red, and 1 yellow tile.

Check

Look back. The answer makes sense for the facts given. So, the answer is correct.

GLE 0406.1.5 Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions. GLE 0406.3.2 Use mathematical language and modeling to develop descriptions, rules and extensions of patterns. Also addresses SPI 0406.3.2.

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Refer to the problem on the previous page. 1. How do you identify a pattern in a problem-solving situation? 2. If Amado and his dad used 36 tiles, how many tiles would they use of each color?

3. Suppose Amado and his dad laid 3 more rows of tiles. How many green tiles would they need in all? 4. Look back at Exercise 3. Check your answer. Explain how you know the answer is correct. EXTRA

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Solve. Use the look for a pattern strategy. 5. Draw the next three figures in the pattern below. Explain.

9. Describe the pattern below. Then find the missing number. 2, 4, 8, , 32

6. Algebra Copy and complete the table. What is the pattern? Input (g)

Output (h)

6

24

8

32

5

20

3

10. Two hikers take turns carrying a backpack. The first hiker carries the pack. They change every 3 miles. They have hiked 14 miles so far. How many times have they changed? Who has the pack now? 11. Algebra A pattern of figures is shown below. Draw the next two figures. Explain your pattern.

36 1 7. Claudia draws a pattern with polygons. She draws a triangle, a quadrilateral, a pentagon, and a hexagon. What polygon should Claudia draw next? 8. Ming found 8 seashells on the first day, 20 on the second day, and 32 on the third day. If the pattern continues, how many shells will she find on the fifth day?

3

5

12. Geometry A border on a scrapbook page has a repeating design that shows a triangle, a pentagon, and a hexagon. Draw the first eight figures in the pattern. 13.

E

WRITE MATH Create a pattern with geometric figures. Give it to a classmate and see if he or she can continue it.

To assess mastery of SPI 0406.4.5, see your Tennessee Assessment Book.

503

Multi-Part Lesson

2

Angles

PART

A

B

Classify Angles Main Idea I will explore angles.

Angles are measured in degrees. You can use circles to help you measure angles.

Materials construction paper

Make a tool to show a 180° angle.

Step 1

Draw two circles. Use a compass or a circle-shaped object to draw two circles of the same size on two different colored pieces of construction paper.

Step 2

Cut out the circles. Cut out each circle.

Step 3

Cut lines in the circles. Cut a straight line halfway through each circle.

Step 4

Join the circles together. Face the lines in the circles toward each other. Then join the circles together on the lines. You have created an angle tool that shows a 180° angle.

compass or a circle to trace scissors

Get ConnectED GLE 0406.4.1 Understand and use the properties of lines, segments, angles, polygons, and circles.

180°

504 5


The yellow section and the pink section each represent a 180° angle.

Make tools to show 45°, 90°, and 360° angles.

Step 1

90°

Make a 90° angle tool. Use the angle tool from Activity 1. A 90° angle looks like the corner of a book. Rotate the circles so that A 90˚ angle is classified as one color represents 90°. a right angle.

Step 2

45°

Make a 45° angle tool. Fold the yellow section (90°) in half. The new angle formed represents a 45° angle.

A 45˚ angle is classified as an acute angle.

Step 3

360°

Make a 360° angle tool. Unfold the paper. Rotate the circles until you see only the yellow section.

About It 1. What happens to the angles as the degrees increase? 2. Would an angle that measures 50° be acute, obtuse, or right?

and Apply It Use the tools you made in Activities 1 and 2 to classify each angle from the real-world object. Use acute, obtuse, or right. 3.

4.

5. corner of your math book

6. angle between two fingers on the same hand

7.

E

WRITE MATH How did you classify the angle described in Exercise 6? Explain. Lesson 2A Angles 505

Multi-Part Lesson

2

PART

Angles A

Main Idea I will identify, describe, and classify angles.

Vocabulary V

B

Angles An angle is a figure made from two rays that have the same endpoint. Angles are measured in degrees (°).

angle right angle

endpoint

acute angle obtuse angle

Get ConnectED GLE 0406.4.1 Understand and use the properties of lines, segments, angles, polygons, and circles. Also addresses GLE 0406.1.7.

Turns and Angles

90°

1 _ turn

_3 turn 270°

1 _ turn

180°

4

2

360°

full turn

4

Turns and Angles MEASUREMENT Brent started his homework at 4:00 P.M. He completed it at the time shown. Write how far the minute hand has turned in degrees and as a fraction. Compare the angle shown on the clock to the angles shown in the Key Concept box.

10 9 8

2 1 11 12

7 6 5

1 So, the angle shown on the clock is 90°, or a _ turn. 4

506 5


2 3

Types of Angles

A right angle measures 90°. This symbol means right angle.

A corner, like the corners on a desk, is a right angle.

An acute angle measures greater than 0° and less than 90°. An obtuse angle measures greater than 90°, but less than 180°.

Classify an Angle Classify each angle as right, acute, or obtuse.

The angle is 90°. So, it is a right angle.

The angle is greater than 90° and less than than 180°. So, it is an obtuse angle.

Write i the measure of each angle in degrees and as a fraction. See Example 1 1.

2.

3.

Classify each angle as right, acute, or obtuse. See Examples 2 and 3 4.

7.

5.

E

6.

TALK MATH Describe what makes each type of angle an acute,

an obtuse, or a right angle. Lesson 2B Angles 507

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Write the measure of the angle in degrees and as a fraction. See Example 1 8.

9.

10.

Classify each angle as right, acute, or obtuse. See Examples 2 and 3 11.

12.

13.

15. Classify the angle shown on the gas gauge below.

14. The timer is set to 30 minutes. How many degrees will the dial have turned when the timer goes off? Use the information to solve the problem.

Tricky Turns

I just did a half turn. That’s a 360°.

Remember, Andrew showed me a trick on his skateboard. He thinks he did a 360°, but I don’t think he did.

I think a half turn actually equals 180°.

16. Is Andrew or Teresa correct? Explain.

17. OPEN ENDED Draw and measure three different angles. 18.

508 5

E

WRITE MATH Describe the graph shown. Write the measure of each angle in degrees and as a fraction.


Number of Pets None One Two

Mid-Chapter Check Tell the number of faces, edges, and vertices. Identify each figure. (Lesson 1B) 1.

8. MULTIPLE CHOICE What is this figure called? (Lesson 1A)

2.

F. hexagon G. triangle H. octagon I.

3. Identify the threedimensional figure the net would make.

Use the look for a pattern strategy to solve. (Lesson 1C) 9. Describe the pattern in 3, 9, 27, , 243. Then find the missing number.

(Lesson 1B)

Identify each polygon. (Lesson 1A) 4.

pentagon

5.

6. MULTIPLE CHOICE Look at the figures below. Which statement is true? (Lesson 1A)

A. There is one polygon.

10. A ferry leaves a harbor every 35 minutes starting at 6:30 A.M. Davion plans to take the first ferry after 8 A.M. When will his ferry leave? Write the measure of each angle in degrees and as a fraction. (Lesson 2B) 11.

12.

B. These are all polygons.

Classify each angle as right, acute, or obtuse. (Lesson 2B)

C. There are two polygons.

13.

D. None of these are polygons. 14. 7. Identify two polygons on the birdhouse. (Lesson 1A)

15.

E

WRITE MATH Can a figure be

a polygon and three-dimensional? Explain. (Lesson 1B) Mid-Chapter Check 509

Multi-Part Lesson

3

Triangles and Quadrilaterals

PART

A

Main Idea I will identify, describe, and classify triangles.

Vocabulary V

B

C

D

E

Triangles There are many different types of triangles. You can classify triangles by the measure of their angles.

right triangle acute triangle

Classify Triangles by Angles

obtuse triangle isosceles triangle equilateral triangle scalene triangle

Get ConnectED

A right triangle has one right angle.

GLE 0406.4.1 Understand and use the properties of lines, segments, angles, polygons, and circles. SPI 0406.4.4 Identify acute, obtuse, and right angles in 2-dimensional shapes.

An acute triangle has three acute angles.

An obtuse triangle has one obtuse angle.

Classify by Angles This sandwich is cut in half. Classify the triangle represented by the half sandwich. The half sandwich has a corner with a right angle. The triangle is a right triangle.

Classify the triangle. Use right, acute, or obtuse.

Since there is one obtuse angle, the triangle is obtuse.

510 5


Triangles can also be classified by the measure of their sides. Classify Triangles by Sides

At least two sides of an isosceles triangle are the same length.

2 ft

2 ft 3 ft

All sides of an equilateral triangle are the same length.

2 ft

2 ft 2 ft

2 ft

No sides of a scalene triangle are the same length.

3 ft 4 ft

Classify by Angles and Sides Classify the triangle. Use acute, rright, or obtuse and isosceles, equilateral, or scalene. The triangle has three angles that are less than 90°. The triangle is acute. All of the sides are the same length, so it is also equilateral.

An acute angle is less than 90° and an obtuse angle is greater than 90°.

Classify l if each triangle. Use acute, right, or obtuse and isosceles, equilateral, or scalene. See Examples 1–3 1.

3 cm 3 cm

2.

3. 7 ft

7 ft

4 in.

5 in.

5 cm 7 ft

3 in.

4. What type of triangle is the pennant? 5.

E

TALK MATH Two sides of an equilateral triangle

measure 3 feet. What is the measure of the third side? Explain. Lesson 3A Triangles and Quadrilaterals

511

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Classify each triangle. Use acute, right, or obtuse and isosceles, equilateral, or scalene. See Examples 1–3 6.

7. 2 in.

2 in.

8.

4 yd

12 ft

2 yd

3 yd 15 ft

2 in.

9 ft

12 cm

9.

10 cm

10.

11.

10 ft

9 yd

4 cm

9 yd

8 ft 6 ft 9 yd

12. Describe the triangle formed by the ladder and the wall.

13. Classify the triangle g on the wedge of cheese.

14. Measurement Shonda draws an equilateral triangle with 2 sides whose sum equals 12 inches. What is the length of the third side?

15. Measurement Ross draws an isosceles triangle with sides 5 centimeters and 3 centimeters. What could the measure of the third side be?

6

in

.

6 in

.

9 in.

Grand Canyon

Phoenix is the capital of Arizona. It has the greatest population of any capital city in the United States.

Flagstaﬀ

ARIZONA Phoenix

16. Classify the triangle formed by Phoenix, Yuma, and the Grand Canyon. 17. Explain how you classified the triangle in Exercise 16.

512 5


Mesa Yuma Tucson

OPEN ENDED Draw an example of each triangle. 18. right scalene triangle

19. obtuse isosceles triangle

20. WHICH ONE DOESN’T BELONG? Identify the term that does not belong with the other three. Explain.

right 21.

obtuse

scalene

acute

E

WRITE MATH Can an equilateral triangle be obtuse? Explain your answer.

Test Practice 22. In the figure, which two angles appear to be obtuse? (Lesson 2B) 1 2

23. What kind of triangle always has 3 acute angles and 3 sides the same length? (Lesson 3A) F. isosceles

4 3

G. right

A. Angles 1 and 2

H. equilateral

B. Angles 1 and 3

I. scalene

C. Angles 1 and 4 D. Angles 2 and 4

Classify each angle as right, acute, or obtuse. (Lesson 2B) 24.

25.

26.

27. Suppose the pattern at the right was extended to 30 figures in all. How many pentagons and octagons would there be? (Lesson 1C) 28. Kolina repeats the pattern shown four times. How many polygons will she use? (Lesson 1C) Lesson 3A Triangles and Quadrilaterals

513

Multi-Part Lesson

3

PART

Triangles and Quadrilaterals A

Main Idea I will identify, describe, and classify quadrilaterals.

B

C

D

E

Quadrilaterals All quadrilaterals have 4 sides and 4 angles.

Vocabulary V

Quadrilaterals

rectangle square rhombus parallelogram trapezoid

Get ConnectED GLE 0406.4.1 Understand and use the properties of lines, segments, angles, polygons, and circles.

A rectangle has 4 right angles with opposite sides equal and parallel. A square has 4 right angles with opposite sides parallel. All sides are equal in length. A rhombus has 4 equal sides with opposite sides parallel.

These marks show equal sides.

A parallelogram has opposite sides equal in length and parallel. A trapezoid has exactly 1 pair of parallel sides.

Classify a Quadrilateral Classify the quadrilateral game board in as many ways as possible.

It can be classified as a parallelogram, a rectangle, a square, and a rhombus.

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Many real-world objects have the shapes of quadrilaterals.

Real-World Shapes VIDEO GAMES Write the type of quadrilateral that best describes the figure around the game controller. The figure has one pair of parallel sides. So, it is a trapezoid. Identify the red figure in as many ways as possible. The figure has 4 right angles, with opposite sides equal and parallel. So, it is a rectangle and a parallelogram.

Classify Cl if each quadrilateral in as many ways as possible. See Example 1

1.

2.

3.

Write the type of quadrilateral that best describes the figure. See Examples 2 and 3

4.

7.

5.

E

6.

TALK MATH How are a square and a rhombus alike? How are

they different? Lesson 3B Triangles and Quadrilaterals 515

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Classify each quadrilateral in as many ways as possible. See Example 1 8.

9.

10.

11.

12.

13.

Write the type of quadrilateral that best describes the figure. See Example 2 and 3

14.

15.

16.

17.

18.

19.

20. A quadrilateral has 4 sides with opposite sides parallel and 4 right angles. Two sides are longer than the others. What is the quadrilateral?

21. Phillip draws a quadrilateral. All 4 sides are the same length. Its opposite sides are parallel. What figure did he draw?

22. OPEN ENDED Draw two quadrilaterals that can be classified as parallelograms. REASONING Tell whether each statement is true or false. If the statement is false, draw a counterexample. 23. A rhombus is a square. 25.

516 5

24. A rectangle is a parallelogram.

E

WRITE MATH True or false: All squares are rectangles, but not all rectangles are squares. Explain. Identify and Describe Geometric Figures

Test Practice 26. Which is not a name for the quadrilateral shown? (Lesson 3B)

27. Sam draws a quadrilateral. It has one pair of parallel sides. It has 2 sides equal in length. What figure did Sam draw? (Lesson 3B) F. rhombus G. square

A. square

C. rectangle

H. trapezoid

B. rhombus

D. trapezoid

I. parallelogram

28. Which statement about these figures is true? (Lesson 1A)

29. Which figure can form a cube when folded on the dotted lines without overlapping? (Lesson 1B) F.

H.

G.

I.

A. There is one polygon. B. There are two polygons. C. These are all polygons. D. None of these are polygons.

30. Jordan draws an equilateral triangle. The sum of the three sides equals 24 inches. What is the length of each side? (Lesson 3A) Identify each figure. Then tell the number of faces, edges, and vertices. (Lesson 1B) 31.

32.

33.

34.

Lesson 3B Triangles and Quadrilaterals 517

Multi-Part Lesson

3

PART

Triangles and Quadrilaterals A

B

C

Problem-Solving Investigation Main Idea I will choose the best strategy to solve a problem.

ARTURO: I have the five puzzle pieces shown. I need to form a square using all of the pieces.

YOUR MISSION: Arrange the five puzzle pieces to form a square.

Understand You know there are five puzzle pieces. Find how to arrange the pieces to form a square.

Plan

Use the act it out strategy. Trace the pieces and cut them out of paper. Then arrange the polygons in different ways to figure out how they will form a square.

Solve

Arrange the pieces in different ways until you form a square.

Check

Look back. The figure formed by the pieces is a square because it is a rectangle that has four equal sides. So, the answer is correct.

GLE 0406.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. Also addresses GLE 0406.3.2.

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• Make a table • Act it out. • Guess, check, and revise.

Use any strategy to solve each problem. 1. Measurement Keli can run 3 miles in 36 minutes. She plans to run each mile one minute faster every 2 weeks. Is it reasonable to say that Keli will be able to run 3 miles in 25 minutes in 3 weeks? Explain.

6. Measurement Kala wants to download 12 songs on her digital music player. She has only 5 minutes to download the songs. If it takes 30 seconds for Kala to download one song, will she have enough time to download all of the songs? Explain. 7. Algebra The polygons below form a pattern. How many sides will the ninth polygon have? Explain.

3

2. Identify a combination of four bills that is worth a total of $50.

3. Algebra Draw the next three figures in the pattern below.

5

7

9

8. Mason has $12. He earns $5 every week for doing chores. Is it reasonable to say that Mason will be able to buy a skateboard that costs $60 in 10 weeks? Explain. 9. A number is multiplied by 2. Then 4 is subtracted from the product. The result is 8. What was the original number?

1

4

9

16 10. Geometry How many different rectangles can you make using all of the squares shown below?

4. Audrey had 8 trading cards. She then bought some packs with 6 cards in each pack. Audrey now has 44 cards. How many packs did she buy?

5. Kareem has $20. He wants to buy the items shown. Will he have enough money? Explain

$9

$4

$8

11.

E

WRITE MATH Look at Exercise 7. Which problem-solving strategy did you use to find the answer? Explain how you used this strategy to solve the problem.

To assess mastery of SPI 0406.4.4, see your Tennessee Assessment Book.

519

in Art

Mosaics are works of art created by pieces of material such as tile, stone, pottery, or brick. Some mosaics are made with geometric figures. Others are made from broken bits of material and do not

Four thousand years ago, terra cotta cones were pushed point-first into a background to create mosaic decorations.

520


show geometric figures. Today, mosaics are used as decoration on floors, tables, walls, and even on the bottom of pools.

Create mosaics using the given polygons. rectangles

trapezoids and obtuse triangles

isosceles triangles, equilateral triangles, and scalene triangles

acute triangles, squares, and rhombuses

right triangles and parallelograms

Problem Solving in Art

521

You will lll need: n 9 index cards, whiteboard, ar ards, whiteboa oard, marker

Geometric Sketch Draw Figures

Get Ready! Players: 2

polygon

right angle

Get Set!

quadrilateral pentagon hexagon

acute angle obtuse angle rectangle

parallelogram trapezoid heptagon nonagon decagon

square rhombus scalene triangle equilateral triangle

Cut the cards in half. Then label the cards with the terms shown.

Go! Shuffle the cards. Then spread the cards facedown on the table. Player 1 turns over a card and draws the figure. If the drawing is correct, Player 1 keeps the card. If Player 1 cannot draw the figure, Player 2 is given a chance to draw the figure. Player 2 keeps the card if he or she can draw the figure. If he or she cannot, the card is put back. Player 2 selects a card. Continue playing until all cards are gone. The player who collects the most cards wins.

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isosceles triangle

Chapter Study Guide and Review Be sure the following Key Concepts are noted in your Foldable.

Key Vocabulary angle polygon three-dimensional figure

Ide nt a ify De nd Ge scrib om e Fig etric ure s

1

2 3 4

two-dimensional figure

5 1-6

Vocabulary Check Choose the vocabulary word that completes each sentence.

Key Concepts Two- and Three-Dimensional Figures • A two-dimensional figure is a plane figure with length and width. (Lesson 1)

1. A(n) figure.

?

is a solid

? 2. A(n) is a figure made from two rays that have the same endpoint.

• A three-dimensional figure is a solid figure with length, width, and height. (Lesson 1)

? is a closed plane 3. A(n) figure that has three or more line segments.

Angles

? has length, 4. A(n) width, and height.

• An angle is a figure made from two rays that have the same endpoint. (Lesson 2)

? 5. A(n) is a plane figure that has length and width.

Quadrilaterals • All quadrilaterals have 4 sides and 4 angles. (Lesson 3)

? 6. A(n) degrees (°).

is measured in

Chapter Study Guide and Review 523

Chapter Study Guide and Review

Lesson 1


Two-Dimensional Figures

(Lessons 1A)

Tell whether each shape is a polygon.

Identify each polygon. 7.

8.

EXAMPLE 1

Tell whether the shape is a polygon. 9.

The moon has curved sides. So, it is not a polygon. EXAMPLE 2

10.

This figure has 8 sides. The sides are straight. So, it is a polygon.

Three-Dimensional Figures

(Lesson 1B)

Identify each figure. Then tell how many faces, edges, and vertices it has. 11.

12.

EXAMPLE 3

Identify the shape of the cooking pot. Then tell the number of faces, edges, and vertices. The cooking pot is a cylinder. It has 2 faces, 0 edges, and 0 vertices.

Problem-Solving Strategy: Look for a Pattern Solve. Use the look for a pattern strategy. 13. Copy and complete the pattern. What are the next two figures in this pattern?

14. The pattern below can also be shown as 1, 4, 7, 10. Draw the next two figures. What are the next two numbers?

524


(Lesson 1C)

EXAMPLE 4

Bruce is creating the pattern below on a bowl in art class. There is enough space for the pattern to repeat three times. How many stars will he make?

The pattern is sun, star, moon, moon, star, sun. There are 2 stars in the pattern before it repeats. So, the number of stars Bruce will make after the pattern repeats three times is 2 × 3, or 6.

Lesson 2

Angles

Angles

(Lesson 2A and 2B)

Write the measure of each angle in degrees and as a fraction of a full turn. 15.

16.

Classify each angle as right, acute, or obtuse.

EXAMPLE 5

Write the measure of the angle shown below in degrees and as a fraction of a full turn.

The angle shown is 360°, or a full turn.

17.

18.

Lesson 3


Triangles

(Lesson 3A)

Classify each triangle. Use acute, right, or obtuse and isosceles, equilateral, or scalene. 19. 2 ft

EXAMPLE 6

Classify the triangle. Use acute, right, or obtuse and isosceles, equilateral, or scalene.

2 ft 4 cm 2 ft

20.

3 cm

8 cm 6 cm 4 cm

6 cm

The triangle has one obtuse angle, so it is obtuse. Since no sides are the same length, the triangle is scalene.

Chapter Study Guide and Review 525

Chapter Study Guide and Review

Lesson 3


Quadrilaterals

(continued)

(Lesson 3B)

Classify each quadrilateral in as many ways as possible. 21.

22.

23.

24.

EXAMPLE 7

Classify the quadrilateral in as many ways as possible.

The figure has parallel sides. So, it is a parallelogram. It has 4 right angles. So, it is a rectangle.

25.

26.

So, the quadrilateral can be classified as a parallelogram and as a rectangle.

Problem-Solving Investigation: Choose a Strategy

(Lesson 3C)

Use any strategy to solve.

EXAMPLE 8

27. Draw the next two figures in the pattern.

Students are lining up by birthdays. Nathan is first in line. His birthday is in September. Beatriz was born in December. Ruby was born after Carlie. Carlie was born in October. What is the order of the students?

28. Liana rounds a number to the nearest hundred and gets 200. What is the least number it could be? the greatest number? 29. Logan has 7 jars of coins. Each jar has 35 coins. How many coins does Logan have?

526


Work backward to solve the problem. Nathan

Carlie

Ruby

Beatriz

September

October

After Carlie

December

So, the order is Nathan, Carlie, Ruby, and Beatriz.

Practice Chapter Test For Exercises 1–3, decide whether each statement is true or false. 1. A square is a two-dimensional figure in which all the sides are the same length.

Classify each triangle. Use acute, right, or obtuse and isosceles, equilateral, or scalene. 8.

9. 3 in.

2. A trapezoid has two pairs of parallel sides. 3. An obtuse triangle has two obtuse angles. 4. Identify the three-dimensional figure the net would make.

13 cm

3 in.

7 cm 7 cm

3 in.

Classify each angle as right, acute, or obtuse. 10.

11.

12. Draw the next two figures in the pattern below. Classify each quadrilateral in as many ways as possible. 5.

6. 13. MULTIPLE CHOICE In the figure below, which angles appear to be acute?

7. MULTIPLE CHOICE How many faces does this figure have?

1 3

2 4

F. Angles 1 and 2 H. Angles 2 and 4 G. Angles 1 and 3 I.

14. A. 3

C. 5

B. 4

D. 6

Angles 3 and 4

E

WRITE MATH Is it possible to draw an isosceles triangle that is acute? Explain. Draw a picture to support your answer. Practice Chapter Test

527

Test Practice

Nara is wrapping a gift in a box shaped like a rectangular prism. How many faces does a rectangular prism have? A. 4

C. 8

B. 6

D. 12

Look for key words. Make sure your answer matches the question being asked.

Read the Question You need to find how many faces a rectangular prism has. Solve the Question Look at the rectangular prism. Count each face. There is 1 face on the top and 1 face on the bottom. There are 4 faces around the figure. 1+1+4=6 So, the rectangular prism has 6 faces. The answer is B.

Read each question. Then fill in the correct answer on the answer sheet provided by your teacher or on a separate sheet of paper. 1. What kind of triangle is shown below?

5 in.

2. Cara drew the following polygon. What polygon did she draw?

5 in.

5 in.

528

A. scalene

C. isosceles

F. decagon

H. nonagon

B. right

D. equilateral

G. hexagon

I. octagon


7. Stanley drew a right angle. Which of the following angles appears to be Stanley’s?

3. Which quadrilateral can be classified as a square and a rhombus? A.

C.

B.

D.

4. Gigi has 4 boxes filled with books. Each box can hold 24 books. How many books does she have? F. 68

H. 96

G. 88

I. 120

8.

F.

H.

G.

I.

GRIDDED RESPONSE Tyrell has 160 pennies. He wants to put the same number of pennies into each jar. How many pennies will be in each jar?

5. Cassie is writing a number pattern. What number comes next in her pattern? 20, 17, 14, 11, 8,

6.

A. 5

C. 3

B. 4

D. 2 9. Mr. Hazel buys groceries for $32.17. If he pays with two twenty-dollar bills, how much change should he receive?

GRIDDED RESPONSE A zoo had 1,295 visitors on Tuesday and 1,523 visitors on Wednesday. How many visitors were there in all on the two days?

A. $8.83

C. $7.93

B. $8.17

D. $7.83

NEED EXTRA HELP? If You Missed Question... Go to Chapter-Lesson... For help with...

1

2

3

10-3A 10-1A 10-3B GLE 4.1

SPI 4.5

SPI 4.5

4

5

6

7

8

4-3E 10-1C 1-3A 10-2B 6-2A GLE 2.2

SPI 3.2

GLE 2.6

SPI 4.4

SPI 2.12

9 9-3E SPI 2.9

Test Practice 529