1. Holt CA Course 1 9-9 Congruent Figures Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 9-9 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° 50° 52°

3. Holt CA Course 1 9-9 Congruent Figures Extension of MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. California Standards

4. Holt CA Course 1 9-9 Congruent Figures Vocabulary Side-Side-Side Rule

5. Holt CA Course 1 9-9 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.

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

7. Holt CA Course 1 9-9 Congruent Figures Identify any congruent figures. B. Additional Example 1: Identifying Congruent Figures in the Real World The sectors in the figure are congruent.

8. Holt CA Course 1 9-9 Congruent Figures Two figures are congruent if they have the same shape and size. Remember!

9. Holt CA Course 1 9-9 Congruent Figures Identify any congruent figures. A. Check It Out! Example 1 The sides of the figures are are not congruent.

10. Holt CA Course 1 9-9 Congruent Figures Identify any congruent figures. B. Check It Out! Example 1 The figures are not congruent. The figure on the outside is larger than the one on the inside.

11. Holt CA Course 1 9-9 Congruent Figures If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent. For triangles, if the corresponding sides are congruent, then the corresponding angles will always be 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.

12. Holt CA Course 1 9-9 Congruent Figures Determine whether the triangles are congruent. Additional Example 2: Identifying Congruent Triangles 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.

13. Holt CA Course 1 9-9 Congruent Figures Determine whether the triangles are congruent. Check It Out! Example 2 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.

14. Holt CA Course 1 9-9 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. If you know that two figures are congruent, you can find the missing measures in the figures.

15. Holt CA Course 1 9-9 Congruent Figures Determine the missing measure in the set of congruent polygons. A. Additional Example 3: Using Congruence to Find Missing Measures The corresponding angles of congruent polygons are congruent. The missing angle measure is 110°.

16. Holt CA Course 1 9-9 Congruent Figures The corresponding sides of congruent polygons are congruent. The missing side length is 28 mm. Determine the missing measure in the set of congruent polygons. B. Additional Example 3: Using Congruence to Find Missing Measures

17. Holt CA Course 1 9-9 Congruent Figures Check It Out! Example 3 Determine the missing measure in the set of congruent polygons. A. 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 length is 4 ft. The corresponding sides are congruent. ?

18. Holt CA Course 1 9-9 Congruent Figures Check It Out! Example 3 Determine the missing measure in the set of congruent polygons. B. 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° ?

19. Holt CA Course 1 9-9 Congruent Figures Lesson Quiz 1. Identify any congruent figures. 2. Determine the missing measures in the set of congruent polygons. none a = 11, b = 6, c = 110°