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Triangle
Congruence Criteria
Essential Question: How can you use triangle
congruence to solve real-world problems?
5
MODULE
LESSON 5.1
Exploring What Makes
Triangles Congruent
LESSON 5.2
ASA Triangle
Congruence
LESSON 5.3
SAS Triangle
Congruence
LESSON 5.4
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Corbis
SSS Triangle
Congruence
REAL WORLD VIDEO
Take a look at some of the
geometry involved in the
engineering marvels of the Golden
Gate Bridge in San Francisco.
MODULE PERFORMANCE TASK PREVIEW
Golden Gate Triangles
In this module, you will explore congruent triangles in the trusses
of the lower deck of the Golden Gate Bridge. How can you use
congruency to help figure out how far apart the two towers of the
bridge are? Let’s find out.
Module 5
217
Are YOU Ready?
Complete these exercises to review the skills you will need
for this chapter.
Angle Relationships
Example 1
• Online Homework
• Hints and Help
• Extra Practice
Line segments AB and DC are parallel. Find the
measure of angle ∠CDE.
A
m∠CDE = m∠ABE Equate alternate
interior angles.
m∠CDE = 33°
33°
Substitute.
60°
B
E
D
C
Find each angle in the image from the example.
1.
m∠BEC
2.
m∠BAE
Congruent Figures
Example 2
Find the length DF. Assume △DEF ≅ △GHJ.
G
D
16 ft
41 ft
113°
E
32 ft
F
J
46°
21°
H
Use the figure from the example to find the given side length or angle measure.
Assume △DEF ≅ △GHJ.
3.
Find the angle m∠GHJ.
4.
Find the length GH.
5.
Find the angle m∠FDE.
6.
Find the length HJ.
Module 5
218
© Houghton Mifflin Harcourt Publishing Company
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Since △DEF ≅ △GHJ, the sides DF and GJ are congruent, or DF ≅ GJ.
Thus, DF = GJ. Since GJ = 41 ft, length DF must also be 41 ft.

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