Classifying Quadrilaterals

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A quadrilateral is a closed shape with 4 straight sides. A trapezoid has exactly 1 pair of parallel sides. or indicates parallel sides. A parallelogram has 2 pairs of.
07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 60

CHAPTER 7

1

Goal

Classifying Quadrilaterals Identify and sort quadrilaterals.

1. Which of these are parallelograms? A

C

B

D

A, C, D

At-Home Help A quadrilateral is a closed shape with 4 straight sides. A trapezoid has exactly 1 pair of parallel sides.

2. Which of these are trapezoids? or E

G

E, G F

indicates parallel sides.

A parallelogram has 2 pairs of parallel sides.

H

3. Draw a quadrilateral that is not a parallelogram or a trapezoid.

A rectangle, a square, and a rhombus are special parallelograms.

Answers will vary. For example:

4. Draw a square. What other shape names can be used to describe a square? and

indicate equal sides.

a parallelogram, a rectangle, a rhombus

60

Answers Chapter 7: 2-D Geometry

Copyright © 2004 Nelson

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CHAPTER 7

2

Goal

Building Quadrilaterals Relate properties of quadrilaterals to their side lengths.

1. Use straws or toothpicks to make these shapes. At-Home Help Draw a picture of each shape. What type of Quadrilaterals can have 4, 3, 2, quadrilateral is each shape? or no equal side lengths. a) a quadrilateral with 4 equal sides and square corners This shape has 3 equal side lengths. Parallelograms have 2 pairs of equal side lengths.

a square b) a quadrilateral with 2 equal long sides and 2 equal short sides, but no square corners

a parallelogram c) a quadrilateral with no equal sides, but 1 pair of parallel sides

a trapezoid d) a quadrilateral with 3 equal sides, but no parallel sides

a quadrilateral Copyright © 2004 Nelson

Answers Chapter 7: 2-D Geometry

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CHAPTER 7

3

Goal

Congruent Shapes Identify and construct congruent shapes.

1. Which shapes are congruent?

At-Home Help 2 shapes are congruent if they are identical in size and shape. C

A

D

B

E

F

A and C B and H D and F

G I

G and I

H

2. Construct a shape congruent to each shape on the grid, using the given line as one side. a)

b)

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Answers Chapter 7: 2-D Geometry

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CHAPTER 7

4

Goal

Similar Shapes Identify and describe similar shapes.

1. Which shapes look similar to the first shape? Explain.

A

B

C

At-Home Help 2 shapes are similar if they are identical in shape, but not necessarily in size.

D

A and D. They are also circles.

2. Which shapes look similar to the first shape? Explain.

F

G

H

E

F and H. They look like they to have 3 equal sides and 3 equal angles like the first triangle. 3. Which shapes look similar to the first shape? Explain.

A

B

C

D

B and D. A is too tall and C is too long.

4. Janice says that congruent shapes are special similar shapes. Do you agree? Why or why not? Yes, congruent shapes are similar shapes that happen to have the same size.

Copyright © 2004 Nelson

Answers Chapter 7: 2-D Geometry

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CHAPTER 7

5

Goal

Measuring Angles Measure angles using a protractor.

1. How many degrees is each angle?

At-Home Help 0 0 18

A protractor is a tool for measuring angles.

30 20 150 10 160 0 17

85°

A

40 140 4 14 0 0 30 15 0

10 20 170 160

0 180

180 0

90

0 10 80

110 70

120 60

130 50

140 40

150 16 30 0 20 17 0 10

0 18 0

170 10

80 70 100 60 110 20 50 0 1 13

This angle is 50°, or 50 degrees.

90

132°

12 0 60 13 50 0

160 20

4 14 0 0

8 10 0 0

30 15 0

100 110 80 70

0 15 30

70 11 0

10 20 170 160

90

0 14 0 4

50 60 130 1 20

0 180

50 0 13

80 70 100 60 110 0 12

100 110 80 70

B

12 0 60 13 50 0

0 14 0 4

0 15 30

160 20

170 10

180 0

140 40

150 16 30 0 20 17 10 0

0 18 0

99°

90

0 10 80

110 70

120 60

130 50

E

8 10 0 0

70

18 0 0

70 110 30 20 150 160 10 0 7 1

90

C

50 60 130 12 0

4 14 0 0

40 140

30 15 0

80 70 100 60 110 20 50 0 1 13

78°

10 20 170 160

D

145°

100 110 80 70

18 0 0

0 180

80 10 0

90

17 0 10

40 140

0

150 160 30 20

11

140 40

50 130 60 120

130 50

30 20 150 10 160 1 70

120 60

0 0 18

110 0 70 10 80

12 0 60 13 50 0

0 14 0 4

0 15 30

160 20

170 10

180 0

64

Answers Chapter 7: 2-D Geometry

Copyright © 2004 Nelson

07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 65

CHAPTER 7

6

Goal

Solve Problems by Acting Them Out

Act out a problem to solve it.

Trace this square and cut out the square you drew. Cut out as many squares as you need to answer the questions below.

At-Home Help A useful problem-solving strategy is to act out a problem. Sometimes you may need to substitute other objects for the ones in the problem. (See Question 1.)

1. 6 square tables are arranged to make 1 long narrow table. 1 person sits on each outside edge of a square table. How many people can sit at the long table? Sketch your answer after you act it out. 14 people

2. How many squares does it take to make a bigger square? Find more than one answer. Sketch your answers after you act them out. For example, 4, 9, 16.

Copyright © 2004 Nelson

Answers Chapter 7: 2-D Geometry

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CHAPTER 7

7

Goal

Lines of Symmetry Draw lines of symmetry.

1. Trace each shape and cut out the shape you drew. Fold it to find a line of symmetry. Unfold it. Repeat to find other lines of symmetry. On this page, draw all the lines of symmetry that you found for each shape.

At-Home Help A line of symmetry is a line that divides a shape in half so if you fold the shape along the line, the halves match.

a)

b) A square has 4 lines of symmetry.

c)

e)

d)

2. Which of the shapes in Question 1 has the most lines of symmetry? The shape in part d), 3 How many? 66

Answers Chapter 7: 2-D Geometry

Copyright © 2004 Nelson

07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 67

CHAPTER 7

8

Goal

Classifying 2-D Shapes Identify and sort 2-D shapes.

1.

At-Home Help B

A

D

C

F

E

2-D shapes can be sorted, or classified, in many different ways. Some of the things you can consider are • the number of sides • whether any sides are equal in length • whether the shapes are congruent • whether there are any parallel sides • whether there are square corners • whether the shape has symmetry

G

J

I H

a) Which shapes have parallel sides? A, B, C, E, G, and H

B and E

b) Which shapes are similar?

B, D, E, G, H, and I

c) Which shapes have symmetry?

2. Describe another way to sort the shapes in Question 1. Which shapes belong? For example, shapes that have 6 sides: C and H. Shapes that have at least 1 right corner: B, E, F, and J. 3. Draw 4 shapes of your own and show 2 ways to sort them. For example: A

B

C

D

Shapes that have 4 sides or more are quadrilaterals: B, C, and D. Shapes that have at least 1 square corner: B and D.

Copyright © 2004 Nelson

Answers Chapter 7: 2-D Geometry

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CHAPTER 7

Test Yourself Circle the correct answer.

B

F

E

C D

A

1. What type of shape is shape D? A. a quadrilateral

B. a trapezoid

C. a rhombus

D. a parallelogram

2. Which shape has more than 2 lines of symmetry? E. shape A

F. shape F

G. shape C

H. shape E

C. shape B

D. shape A

G. shape C

H. shape A

3. Which shape has no parallel sides? A. shape D

B. shape E

4. Which shape is similar to shape E? E. shape F

F. shape B

5. Which of these shapes is congruent to shape A? A.

B.

C.

D.

6. Which of these shape names is not another way of describing a square? E. a rectangle

F. a trapezoid

G. a parallelogram

H. a quadrilateral

7. What is the measure of the angle shown?

180 0

4 14 0 0 10 20 170 160

0 180

12 0 60 13 50 0

170 10

Answers Chapter 7: 2-D Geometry

100 110 80 70

160 20

68

90

0 15 30

D. 150°

50 0 13

80 70 100 60 110 0 2 1

0 14 0 4

B. 35°

C. 145° 30 15 0

A. 30°

Copyright © 2004 Nelson