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GEOMETRY 2-5 NOTES AUGUST 26, 2016 OR AUGUST 29, 2016 2-5 PROVING ANGLES CONGRUENT • Learning Objectives • Identify angle pairs • Understand and use theorems about angles • Vertical Angles • Two angles whose sides are opposite rays • Adjacent Angles • Two coplanar angles with a common side, a common vertex, and no common interior points 2-5 PROVING ANGLES CONGRUENT • Complementary Angles • Two angles whose measure have a sum of 90°. Each angle is called the compliment of the other. 20° 70° • Supplementary Angles • Two angles whose measures have a sum of 180°. Each angle is called the supplement of the other. 35° 𝟏𝟕𝟓° 2-5 PROVING ANGLES CONGRUENT • From a diagram you CAN assume: • Adjacent angles • Adjacent supplementary angles • Vertical angles • Unless the diagram gives you this information, you CANNOT assume : • Angles or segments are congruent • An angle is a right angle • Lines are parallel or perpendicular • And NEVER assume that anything is drawn to scale unless you are specifically told to use a ruler or protractor to measure 2-5 PROVING ANGLES CONGRUENT • Proof • The set of steps you take to reach a theorem • Theorem • The statement that you prove true • Theorem 2-1: • Vertical Angles Theorem • Vertical angles are congruent ∠1≅∠2 and ∠3≅∠4 1 3 4 2 2-5 PROVING ANGLES CONGRUENT • Theorem 2-2: • Congruent Supplements Theorem • If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. Proof on pg. 99 2-5 PROVING ANGLES CONGRUENT • Theorem 2-3: • Congruent Complements Theorem • If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent • Theorem 2-4: • All right angles are congruent • Theorem 2-5: • If two angles are congruent and supplementary, then each is a right angle HOMEWORK 2-5 Pg. 100 # 1-18, 20-25, 39-42