Understanding Quadrilaterals and Measuring Angles

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This pdf help us in understanding quadrilaterals on the basis of angle and shapes with detailed explanation.

1. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 60
CHAPTER 7
1 Classifying Quadrilaterals
Goal Identify and sort quadrilaterals.
1. Which of these are parallelograms? At-Home Help
A quadrilateral is a closed shape
A C A, C, D with 4 straight sides.
A trapezoid has exactly 1 pair
B D of parallel sides.
2. Which of these are trapezoids?
or indicates parallel sides.
E G A parallelogram has 2 pairs of
E, G parallel sides.
F H
A rectangle, a square, and a
3. Draw a quadrilateral that is not a parallelogram rhombus are special
parallelograms.
or a trapezoid.
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

2. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 61
CHAPTER 7
2 Building Quadrilaterals
Goal 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 61

3. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 62
CHAPTER 7
3 Congruent Shapes
Goal 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 B
D 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)
62 Answers Chapter 7: 2-D Geometry Copyright © 2004 Nelson

4. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 63
CHAPTER 7
4 Similar Shapes
Goal Identify and describe similar shapes.
1. Which shapes look similar to the first shape? At-Home Help
Explain. 2 shapes are similar if they are
identical in shape, but not
necessarily in size.
A B C D
A and D. They are also circles.
2. Which shapes look similar
to the first shape? Explain. G
F
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 63

5. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 64
CHAPTER 7
5 Measuring Angles
Goal Measure angles using a protractor.
1. How many degrees is each angle? At-Home Help
A protractor is a tool for
0 0
18
measuring angles.
10
85°
17
0
20
160
A
30
150
80 100
70 90 110
100 80
140
12
40
60 110 70 0
0 60 13
50 0 12
50 0
130 1
13
50
14 0
14 0
0
4
4
0
20
60
15
30
0
30
0
15
11
160
70
20
0
160
20
10 0
0
170
8
170
10
10
18 0
90
0
10
180
0
180
80
10
0
0
0
20 20 17 10
180
70
170 30 0 0
160 30 16 40 50 60 110
15 4 150 120
0
14 0
140 130
0
50 0 1
13
This angle is 50°, or 50 degrees.
60
20
70
110
132°
100
80
90
B
100
80
70
110
60
12
0
50 0
13
4
14 0
30 0
20 15
10 0
0 160
170
180
0
18 0
10 0
17
0
16
20
99°
150
30
140
E
40
130
50
120
60
70
110
80
0
10
90
0
10 0 18
8 0
11 1 70 0 0
70 120 10 160
130 60 140 150
50 20
40 30
130 140 150
120 40 160
50 30
110 60 20 17
0 70 0 18
10 10
80 0 0
90
80
0
0
10
10
180 20
170
70
160 30
110
15 4
0
14 0
50 60
0
0
130 12
50 0 1
13
60
140
20
40
70
110
D
150
30
78°
100
80
145°
160
20
C
90
7 0
1
10
100
80
0
18 0
70
110
60
12
0
50 0
13
4
14 0
30 0
20 15
10 0
0 160
170
180
64 Answers Chapter 7: 2-D Geometry Copyright © 2004 Nelson

6. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 65
CHAPTER 7
Solve Problems by Acting
6 Them Out
Goal Act out a problem to solve it.
Trace this square and cut out At-Home Help
the square you drew. A useful problem-solving
strategy is to act out a
Cut out as many squares as
problem. Sometimes you may
you need to answer the need to substitute other objects
questions below. 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 65

7. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 66
CHAPTER 7
7 Lines of Symmetry
Goal Draw lines of symmetry.
1. Trace each shape and cut out the shape you drew. At-Home Help
Fold it to find a line of symmetry. Unfold it. A line of symmetry is a line
Repeat to find other lines of symmetry. that divides a shape in half so if
On this page, draw all the lines of symmetry you fold the shape along the
that you found for each shape. 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?
How many? The shape in part d), 3
66 Answers Chapter 7: 2-D Geometry Copyright © 2004 Nelson

8. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 67
CHAPTER 7
8 Classifying 2-D Shapes
Goal Identify and sort 2-D shapes.
1.
At-Home Help
A B D
C 2-D shapes can be sorted, or
classified, in many different
ways. Some of the things you
F can consider are
E G
• the number of sides
• whether any sides are equal
in length
I J
• whether the shapes are
H congruent
• whether there are any
parallel sides
• whether there are square
corners
a) Which shapes have parallel sides? • whether the shape has
A, B, C, E, G, and H symmetry
b) Which shapes are similar? B and E
c) Which shapes have symmetry? B, D, E, G, H, and I
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 67

9. 07-NEM-GR4-WBAN/SI-CH07 11/3/03 2:50 PM Page 68
CHAPTER 7
Test Yourself
Circle the correct answer.
B C E F
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
3. Which shape has no parallel sides?
A. shape D B. shape E C. shape B D. shape A
4. Which shape is similar to shape E?
E. shape F F. shape B G. shape C H. shape A
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?
80 100
A. 30° C. 145° 60
20
70
110
100
90 80
110
70 12
60
0
13
50 0 1
50 0
13
14 0
14 0
B. 35° D. 150°
0
4
4
0
15
30
0
30
0
15
160
20
160
20
170
170
10
10
180
180
0
0
68 Answers Chapter 7: 2-D Geometry Copyright © 2004 Nelson

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