1. 7-5 Congruent Figures Warm Up
Find the measure of the third angle in the triangle, given two angle measures.
1. 58°, 104°
2. 32°, 63°
3. 90°, 38°
4. 42°, 88°
18°
85° 90
52°
50°
Course 2

2. 7-5
Congruent Figures
Objective Today
You will learn to identify congruent figures and to use them to find missing measures.
Key Math Term Congruent polygons – Are polygons with the same shape and the same size
Course 2

3. Course 2
7-5
Congruent Figures
If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent. For triangles in particular, the corresponding angles will always be congruent if the corresponding sides are congruent. This is called the Side-Side-Side Rule. Because of this rule, when determining whether triangles are congruent, you only need to determine whether the sides are congruent.

4. Example 1: Identifying Congruent Triangles
7-5
Congruent Figures
Example 1: Identifying Congruent Triangles
Determine whether the triangles are congruent. C Q
4 cm
4 cm
AB = 4 cm
BC = 4 cm
AC = 6 cm
PQ = 4 cm
PR = 4 cm
RQ = 5 cm B P
6 cm
5 cm
4 cm
4 cm R A
The triangles are not congruent. Although two sides in one triangle are congruent to two sides in the other, the third sides are not congruent.
Course 2

5. 7-5 Congruent Figures Try This: Example 2
Determine whether the triangles are congruent.
AC = 8 m
AB = 6 m
BC = 10 m
DF = 8 m
DE = 6 m
EF = 10 m B E
10 m
10 m
6 m
6 m A C F D
8 m
8 m
By the Side-Side-Side Rule, ABC is congruent to DEF, or
ABC  DEF. If you flip one triangle, it will fit exactly over the other.
The notation ABC is read “triangle ABC.”
Reading Math
Course 2

6. 7-5
Congruent Figures
For polygons with more than three sides, it is not
enough to compare the measures of their sides.
For example, the corresponding sides of the
figures below are congruent, but the figures are
not congruent.
120 m
70 m
120 m
70 m
145°
35°
35°
145°
If you know that two figures are congruent, you
can find the missing measures in the figures.
Course 2

7. Additional Example 3A: Using Congruence to Find Missing Measures
7-5
Congruent Figures
Additional Example 3A: Using Congruence to Find Missing Measures
Determine the missing measures in the set of congruent polygons.
The corresponding
sides are congruent.
The missing side measure is 28 mm.
Course 2

8. Additional Example 3B: Using Congruence to Find Missing Measures
7-5
Congruent Figures
Additional Example 3B: Using Congruence to Find Missing Measures
Determine the missing measure in the set of congruent polygons.
The corresponding angles are congruent.
The missing angle measure is 88°.
Course 2

9. Insert Lesson Title Here
Course 2
7-5
Congruent Figures
Insert Lesson Title Here
Try This: Example 3A
Determine the missing measure in the set of congruent polygons.
135°
The corresponding
sides are congruent.
5 ft
120°
6 ft
45°
60°
8 ft
The missing side
measure is 4 ft.
8 ft
60°
45°
6 ft
5 ft
135°
120°
4 ft

10. Insert Lesson Title Here
7-5
Congruent Figures
Insert Lesson Title Here
Try This: Example 3B
Determine the missing measure in the set of congruent polygons.
6 ft
5 ft
130°
110°
8 ft
The corresponding
angles are congruent.
120°
80°
4 ft
100°
10 ft
The missing angle
measure is 130°.
10 ft
100°
4 ft
80°
120°
8 ft
110° ?
5 ft
6 ft
Course 2

11. Insert Lesson Title Here
7-5
Congruent Figures
Insert Lesson Title Here
Lesson Quiz
1. Are the triangles congruent? no F D E
5 cm
8 cm A B C
7 cm
5 cm
8 cm
2. Determine the missing measures for the
set of congruent polygons. 11
70°
70°
110° c 6 6 6 b
70°
110°
70°
110° 18 a
a =11, b =6, c = 110°
Course 2