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2-5 Proving Angles Congruent M11.B.2 2.5.11.C OBJECTIVES: 1) TO IDENTIFY ANGLE PAIRS 2) TO PROVE AND APPLY THEOREMS ABOUT ANGLES 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 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 Example: Identifying Angle Pairs 2 1 3 4 • Name all pairs of angles a) Vertical: b) Supplementary: c) Complementary: Example: Identify Angle Pairs Complementary: Supplementary: Vertical: 2 1 5 3 4 Assumptions from Diagram **Things you can conclude from a diagram: 1) Adjacent angles 2) Adjacent supplementary angles 3) Vertical angles 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 Example: Making Conclusions from a Diagram True or False 1) < 3 is a right angle 2) < 1 and < 5 are adjacent 3) < 3 = < 5 4 3 2 5 1 Vertical Angle Theorem Vertical angles are congruent. Example: Find the value of x 2x - 3 4x - 10