Download 8.5 Practice with Examples

LESSON
8.5
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 488–496
GOAL
Use similarity theorems to prove that two triangles are similar
VOCABULARY
Theorem 8.2 Side-Side-Side (SSS) Similarity Theorem
If the corresponding sides of two triangles are proportional, then the
triangles are similar.
Theorem 8.3 Side-Angle-Side (SAS) Similarity Theorem
If an angle of one triangle is congruent to an angle of a second triangle
and the lengths of the sides including these angles are proportional, then
the triangles are similar.
EXAMPLE 1
Using the SSS Similarity Theorem
Which of the following triangles are similar?
A
3
B
E
4
C
4
G
4
3
10
D
5
F
6
J
8
H
SOLUTION
To decide which, if any, of the triangles are similar, you need to consider the
ratios of the lengths of corresponding sides.
Ratios of Side Lengths of ABC and DEF
CA
3
DF 5
Longest sides
AB 2 1
EF 4 2
Remaining sides
Chapter 8
BC
1
DE 3
Shortest sides
Because the ratios are not equal, ABC and DEF are not similar.
Ratios of Side Lengths of GHJ and DEF
GH 6 2
DE
3 1
GJ
10 2
DF
5
1
8 2
HJ
EF 4 1
Shortest sides
Longest sides
Remaining sides
Because the ratios are equal, GHJ ~ DEF.
Since DEF is similar to GHJ and DEF is not similar to ABC, GHJ is
not similar to ABC.
Copyright © McDougal Littell Inc.
All rights reserved.
Geometry
Practice Workbook with Examples
151
LESSON
8.5
CONTINUED
NAME _________________________________________________________ DATE ____________
Reteaching with Practice
For use with pages 488–496
Exercises for Example 1
Determine which two of the three given triangles are similar.
1.
B
F
8.5
17
8
D
A
20
10
9
G
4
H
6
8
E
J
C
2. J
N
6
L
9.1
M
7.2
P
11.2
8
S
Chapter 8
K
Q
5
7
R
9.6
6
152
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.
LESSON
8.5
CONTINUED
EXAMPLE 2
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 488–496
Using the SAS Similarity Theorem
Use the given lengths to prove that ABC ~ DEC.
E
16
B
4C
A
SOLUTION
3
12
D
Begin by finding the ratios of the lengths of the corresponding sides.
BC
4
1
EC 16 4
AC
3
1
DC 12 4
So, the side lengths AC and BC of ABC are proportional to the corresponding
side lengths DC and EC of DEC. The included angle in ABC is BCA; the
included angle in DEC is ECD. Because these two angles are vertical angles,
they are congruent. So, by the SAS Similarity Theorem, ABC ~ DEC.
Exercises for Example 2
Prove that the two triangles are similar.
3.
4.
E
P
D
5.
10
T
Q
4
11
16
12.8
A 4 B
U
6
N
S
9
9
R
10
C
R
6
V
Chapter 8
20
M
Copyright © McDougal Littell Inc.
All rights reserved.
Geometry
Practice Workbook with Examples
153