1. 4.2 Angle Relationships in Triangles

2. http://my.hrw.com/math11/math06_07/nsme dia/practice_quizzes/geo/geo_pq_trc_01.html http://my.hrw.com/math11/math06_07/nsme dia/practice_quizzes/geo/geo_pq_trc_01.html

3. Goals for today! Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles.

4. Exploration Materials: Notecard, ruler, and scissors

5. Theorem/Postulate Page

6. Example 1 mXYZ + mYZX + mZXY = 180° mXYZ + 40 + 62 = 180 mXYZ + 102 = 180 mXYZ = 78° 2. Find m  YWZ. 1. Find m  XYZ mYXZ + mWXY = 180° 62 + mWXY = 180 mWXY = 118°

7. A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

8. Theorem/Postulate Page

9. Example 2 The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle? HINT: DRAW A PICTURE m  A + m  B = 90° 63.7 + m  B = 90 m  B = 26.3°

10. Interior and Exterior

11. Remote Interior Angles The remote interior angles of  4 are  1 and  2.

12. Theorem/Postulate Page

13. Example 3 Find m  B. m  A + m  B = m  BCD 15 + 2x + 3 = 5x – 60 2x + 18 = 5x – 60 78 = 3x 26 = x m  B = 2x + 3 = 2(26) + 3 = 55°

14. Example 4 Find m  ACD. m  ACD = m  A + m  B 6z – 9 = 2z + 1 + 90 6z – 9 = 2z + 91 4z = 100 z = 25 m  ACD = 6z – 9 = 6(25) – 9 = 141°

15. Theorem/Postulate Page

16. Example 5 Find m  P and m  T. P  TP  T 2x 2 = 4x 2 – 32 –2x 2 = –32 x 2 = 16 So m  P = 2x 2 = 2(16) = 32°. Since m  P = m  T, m  T = 32°.

17. CHECK UP 1.The measure of one of the acute angles in a right triangle is 56°. What is the measure of the other acute angle? 2. Find m  ABD. 3. Find m  N and m  P.

18. Check Up 4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store?

19. Assignment Page 227 4-22 all