Page 1 of 6
Line Symmetry
BEFORE
Now
WHY?
You learned about congruent
and similar figures.
You’ll identify lines of
symmetry.
So you can find the symmetry of a
tennis court, as in Ex. 14.
Create a figure with symmetry.
Word Watch
line symmetry, p. 460
line of symmetry, p. 460
1 Fold a sheet of
paper in half.
2 Cut a design out
of the folded edge
as shown. Unfold
the design.
3 Are the figures
on the opposite
sides of the fold
the same size?
the same shape?
Line Symmetry A figure has line symmetry if a line can be drawn that
divides the figure into two congruent parts that are mirror images of each
other. The line is called the line of symmetry .
EXAMPLE
1
Identifying Lines of Symmetry
Tell whether the object has line symmetry. If so, draw the line of
symmetry.
a.
b.
Yes, this guitar has line
symmetry.
No, this guitar does not
have line symmetry.
Your turn now
Tell whether the figure has line symmetry. If so, copy
the figure and draw the line of symmetry.
1.
460
Chapter 9
Geometric Figures
2.
3.
Page 2 of 6
Lines of Symmetry
A figure can have zero, one, or multiple lines of symmetry.
no lines of
symmetry
EXAMPLE
2
1 line of
symmetry
2 lines of
symmetry
3 lines of
symmetry
Multiple Lines of Symmetry
Find the number of lines of symmetry in a square.
Think about how many different ways you can fold a square in half so
that the two halves match up perfectly.
vertical fold
horizontal fold
diagonal fold
diagonal fold
ANSWER A square has 4 lines of symmetry.
EXAMPLE
3
Completing Symmetrical Figures
Complete the polygon so that it has the line of symmetry shown.
with
Solving
To find the mirror image of
a point in Example 3, find
the distance between the
point and the line of
symmetry. Place the mirror
image point the same
distance from the line of
symmetry, but on the
opposite side.
1 Draw the mirror image of
each vertex that is not on
the line of symmetry.
2 Connect the points to complete
the mirror image so that the two
halves are congruent.
Lesson 9.8
Line Symmetry
461
Page 3 of 6
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 716
Getting Ready to Practice
1. Vocabulary A figure has _?_ if it can be divided by a line into two
congruent parts that are mirror images of each other.
Find the number of lines of symmetry in the object.
2.
3.
4.
Practice and Problem Solving
Tell whether the line shown is a line of symmetry.
5.
6.
7.
Copy the figure and draw all lines of symmetry.
8.
with
Example
1
2
3
Homework
Exercises
5–10
8–10
11–13
11.
CLASSZONE.COM
• More Examples
• eTutorial Plus
Chapter 9
10.
Copy and complete the figure so that it has the line of symmetry
shown.
Online Resources
462
9.
Geometric Figures
12.
13.
Page 4 of 6
14. Find the number of lines of
15. Find the number of lines of
symmetry in the tennis court.
symmetry in the baseball field.
16. Make a Model Copy the figure at the right.
Cut out your copy and use it to find the
number of lines of symmetry in the figure.
17. Critical Thinking Is there a type of triangle that has exactly one line of
symmetry? If so, identify the type of triangle.
18. Challenge Which quadrilaterals have exactly two lines of symmetry?
Sketch the quadrilaterals and show the lines of symmetry.
Mixed Review
Use mental math to solve the equation. (Lesson 1.6)
19. 12 x 24
20. x 8 22
21. 3x 27
22. x 5 4
1
3
25. 18
2
10
39
26. 13
70
Find the product. (Lesson 7.2)
7
6
23. 12
7
2
1
24. 3
2
Basic Skills Estimate the product.
27. 11 24
28. 9 21
29. 32 72
30. 48 63
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
31. Multiple Choice Which letter has no lines of symmetry?
A.
E
B.
F
C.
T
D.
W
32. Multiple Choice How many lines of symmetry does the letter
F. none
G. one
H. two
Lesson 9.8
H have?
I. four
Line Symmetry
463
Page 5 of 6
9.5 TO
9. 8
Notebook Review
Check Your Definitions
Review the
vocabulary
definitions in
your notebook.
Copy the review
examples in your
notebook. Then
complete the
exercises.
quadrilateral, p. 445
parallelogram, p. 445
rectangle, p. 445
rhombus, p. 445
square, p. 445
congruent, p. 454
similar, p. 454
corresponding parts,
p. 455
line symmetry, p. 460
polygons: pentagon,
hexagon, octagon,
p. 449
regular polygon, p. 450
diagonal, p. 450
Use Your Vocabulary
1. Copy and complete: A _?_ is a quadrilateral with two pairs of parallel sides.
2. Are all rhombuses regular polygons? Why or why not?
9.5–9.6 Can you classify quadrilaterals and polygons?
EXAMPLE Classify the polygon shown.
ANSWER The polygon is a quadrilateral,
a parallelogram, a rectangle, a rhombus,
and a square.
✓ Classify the polygon.
3.
4.
9.7 Can you identify similar and congruent figures?
EXAMPLE The triangles at the right
D
E
are similar. List the corresponding parts.
Z
ANSWER Corresponding angles:
aD and aX, aE and aY, aF and aZ
X
F
Y
E
and XY
, E
F
and YZ
, F
D
and ZX
Corresponding sides: D
D
✓ 5. Tell whether the triangles are similar or
congruent. List the corresponding parts.
464
Chapter 9
Geometric Figures
E
F
C G
H
Page 6 of 6
9.8 Can you find lines of symmetry?
EXAMPLE Tell whether the figure has line
symmetry. If so, draw any lines of symmetry.
ANSWER The figure has one line of symmetry.
✓ Tell whether the line shown is a line of symmetry.
6.
7.
8.
about Lessons 9.5–9.8
9. Writing Your friend says that a regular hexagon is a parallelogram.
Is her statement correct? Explain why or why not.
Review Quiz 2
Classify the polygon in as many ways as possible.
1.
6m
2.
3m
3m
3.
4 ft
3 ft
3 ft
4 ft
6m
4. A regular pentagon has a perimeter of 15 feet. What is the side length?
Use the congruent quadrilaterals shown.
J
M
X
Y
70
5. List the corresponding parts.
a
12 cm
6. Find the value of a.
110
7. What is maK ?
L 11 cm
K
W
Z
Find the number of lines of symmetry in the figure.
8.
9.
10.
Lessons 9.5–9.8
Notebook Review
465