1. 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° Course 2 7-9 Congruent Figures

2. Learn to identify congruent figures and to use congruence to solve problems. Course 2 7-9 Congruent Figures

3. Vocabulary Side-Side-Side Rule Insert Lesson Title Here Course 2 7-9 Congruent Figures

4. Course 2 7-9 Congruent Figures Which center circle do you think is bigger? In spite of appearances, the two center circles are congruent. Their apparent differences are optical illusions. One way to determine whether figures are congruent is to see if one figure will fit exactly over the other one. Look at the two patterns.

5. Identify any congruent figures. Additional Example 1A: Identifying Congruent Figures in the Real World Course 2 7-9 Congruent Figures A. The sides of the octagons are not congruent. Each side of the outer figure is larger than each side of the inner figure.

6. Identify any congruent figures. Additional Example 1B: Identifying Congruent Figures in the Real World Course 2 7-9 Congruent Figures B. The buttons labeled 1, 4, 7, and * are congruent. The buttons labeled 2, 5, 8, and 0 are also congruent. Also the buttons labeled 3, 6, 9, and # are congruent.

7. Course 2 7-9 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.

8. Determine whether the triangles are congruent. Additional Example 2: Identifying Congruent Triangles Course 2 7-9 Congruent Figures 4 cm 6 cm 5 cm 4 cm A B C R P Q AB = 4 cm BC = 4 cm AC = 6 cm PQ = 4 cm PR = 4 cm RQ = 5 cm 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.

9. Determine whether the triangles are congruent. Try This: Example 2 Course 2 7-9 Congruent Figures AC = 8 m AB = 6 m BC = 10 m DF = 8 m DE = 6 m EF = 10 m The notation ABC is read “triangle ABC.” Reading Math A B C F D E 6 m 8 m 10 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.

10. Course 2 7-9 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° If you know that two figures are congruent, you can find the missing measures in the figures.

11. Determine the missing measures in the set of congruent polygons. Additional Example 3A: Using Congruence to Find Missing Measures Course 2 7-9 Congruent Figures The missing side measure is 28 mm. The corresponding sides are congruent.

12. Determine the missing measure in the set of congruent polygons. Additional Example 3B: Using Congruence to Find Missing Measures Course 2 7-9 Congruent Figures The missing angle measure is 88°. The corresponding angles are congruent.

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

14. Try This: Example 3B Determine the missing measure in the set of congruent polygons. Insert Lesson Title Here Course 2 7-9 Congruent Figures The missing angle measure is 130°. The corresponding angles are congruent. 6 ft 8 ft 4 ft 5 ft 4 ft 8 ft 10 ft 120° 130° 110° 100° 80° 110° 80° 100° 120° ?

15. Lesson Quiz 1. Are the triangles congruent? Insert Lesson Title Here Course 2 7-9 Congruent Figures A B C 7 cm5 cm 8 cm F D E 5 cm 8 cm 2. Determine the missing measures for the set of congruent polygons. 18 6 a b 70° 110° 6 6 11 110° 70° no a =11, b =6, c = 110° 70° 110° c

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