Chapter 8 Lesson 2

1
Chapter 8 Lesson 2

• Objective To identify similar polygons.

2
Similar Polygons

• Notes
• Two figures that have the same shape but not
  necessarily the same size are similar ().

• Two figures are similar if
• Corresponding angles are congruent
• Corresponding sides are proportional

• The ratio of the lengths of corresponding sides
  is the similarity ratio.

3
Example 1 Understanding Similarity

• ABCD EFGH. Complete each statement.

a.
53
Corresponding angles are congruent.
b.
Corresponding sides are proportional.
4
Example 2 Understanding Similarity

• ?ABC ?XYZ. Complete each statement.

a.
78
B
Corresponding angles are congruent.
b.
A
C
Corresponding sides are proportional.
Y
78
42
X
Z
5
Example 3 Determining Similarity

• Determine whether the triangles are similar. If
  they are, write a similarity statement and give
  the similarity ratio.

• Remember
• Two figures are similar if
• Corresponding angles are congruent
• Corresponding sides are proportional

All three pairs of angles are congruent by the
markings.
?ABC ?FED Similarity Statement
3 4 or ¾ Similarity Ratio
6
Example 4 Determining Similarity
Determine whether the triangles are similar. If
they are, write a similarity statement and give
the similarity ratio.
Y

• Remember
• Two figures are similar if
• Corresponding angles are congruent
• Corresponding sides are proportional

12
14
X
Z
16
All three pairs of angles are congruent by the
markings.
N
18
21
P
M
24
?XYZ ?MNP Similarity Statement
2 3 or 2/3 Similarity Ratio
7
Example 5 Determining Similarity
Determine whether the parallelograms are similar.
Explain.
K
L
1
2
B
C
120
100
They are not similar because corresponding angles
are not congruent.
2
2
4
4
A
D
J
M
1
2
8
Example 6 Using Similar Figures
LMNO QRST. Find the value of x.
Step 1 Write a proportion.
Step 2 Substitute.
Step 3 Cross Multiply.
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Example 7 Using Similar Figures
LMNO QRST. Find the value of SR.
Step 1 Write a proportion.
Step 2 Substitute.
Step 3 Cross Multiply.
10
Assignment
Pg. 425 1-39 (odd)