1. OBJECTIVES: 1) TO IDENTIFY ANGLE PAIRS 2) TO PROVE AND APPLY THEOREMS ABOUT ANGLES 2-5 Proving Angles Congruent M11.B.2 2.5.11.C

2. Vocabulary Vertical Angles – two angles whose sides form two pairs of opposite rays 1 3 4 2 Adjacent Angles – two coplanar angles with a common side, a common vertex, and no common interior points 1 2

3. Vocabulary Complementary Angles – two angles whose measures have sum 90°. Each angle is called the complement of the other. A 60 B 30 Supplementary Angles – two angles whose measures have sum 180°. Each angle is called the supplement of the other. 3 4 75 105

4. Example: Identifying Angle Pairs Name all pairs of angles a) Vertical: b) Supplementary: c) Complementary: 1 2 3 4

5. Example: Identify Angle Pairs Complementary: Supplementary: Vertical: 2 1 3 5 4

6. Assumptions from Diagram **Things you can conclude from a diagram: 1) Adjacent angles 2) Adjacent supplementary angles 3) Vertical angles

7. Can NOT Assume: (Unless Marked) **Things you cannot conclude from a diagram without markings 1) Angles or segments are congruent 2) An angle is a right angle 3) Lines are parallel or perpendicular

8. Example: Making Conclusions from a Diagram True or False 1) < 3 is a right angle 2) < 1 and < 5 are adjacent 3) < 3 = < 5 1 2 3 4 5

9. Vertical Angle Theorem Vertical angles are congruent.

10. Example: Find the value of x 2x - 3 4x - 10