1. Then/Now You identified isosceles and equilateral triangles. Use properties of isosceles triangles. Use properties of equilateral triangles.

2. Vocabulary legs of an isosceles triangle vertex angle base angles

3. Concept

4. Example 1 Congruent Segments and Angles A. Name two unmarked congruent angles. Answer:  BCA and  A  BCA is opposite BA and  A is opposite BC, so  BCA   A. ___

5. Example 1 Congruent Segments and Angles B. Name two unmarked congruent segments. Answer: BC  BD ___ BC is opposite  D and BD is opposite  BCD, so BC  BD. ___

6. Concept

7. Since QP = QR, QP  QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so m  P = m  R. Use the Triangle Sum Theorem to write and solve an equation to find m  R. Example 2 Find Missing Measures A. Find m  R. Triangle Sum Theorem m  Q = 60, m  P = m  R Simplify. Subtract 60 from each side. Divide each side by 2. Answer: m  R = 60

8. Example 2a A.30° B.45° C.60° D.65° A. Find m  T.

9. Example 2b A.1.5 B.3.5 C.4 D.7 B. Find TS.

10. Example 3 A.x = 20, y = 8 B.x = 20, y = 7 C.x = 30, y = 8 D.x = 30, y = 7 Find the value of each variable.