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Geometry Section 2-5: Proving Angles Congruent Name:_____________ Date:_____ Period:__ Target Goals: I will be able to continue to practice proofs (both two column and paragraph) I will be able to apply theorems about congruent angles in proofs Review from yesterday…. Given: TA is the angle bisector Solve for x and justify each step Step Justification PART ONE: Complete each definition and draw a picture to represent it. Vertical Angles are ____________angles whose sides form two pairs of opposite __________. Picture: Complimentary Angles are two angles where the _________ of their measures is 90. Picture: Supplementary Angles are two angles where the _________ of their measures is 180. Picture: **NOTE** We also refer to supplementary angles as a ________________ _____________. PART TWO: Example 1: Solve for x (2x + 3) (4x – 101)˚ Did you get 52? If so, how did you know that the two expressions were equal? How do we truly know that vertical angles are congruent? Vertical Angle Theorem: Let’s prove this…. Given: < 1 and < 2 are vertical angles Prove: < 1 and < 2 are congruent 3 1 2 Example 2: Solve for y. o o (6y – 10) (6y + 10) Did you get y = 15? If so, how did you know to add the given expressions and set them equal to 180°? How do we truly know that any linear pair adds to 180°? Congruent Supplements Theorem: Let’s prove this… Given: <1 and <2 are supplementary <3 and <2 are supplementary Prove: <1 <3 1 2 3 Example 3: Solve for x. Did you get x = 6? If so, how did you know to add the given expressions and set them equal to 90°? How do we truly know these angles should add to 90°? Congruent Compliments Theorem: Let’s prove this… Given: <1 and <2 are complimentary <3 and <2 are complimentary Prove: <1 <3 Other things you should know… All right angles are:___________________________ If two angles are congruent and supplementary, then each angle must be _______________. Example 4: A and B are complementary angles. Find m A and m B if A is 2 times as large as its complement. You try! A and B are supplementary angles. Find m A and m B if A is 3 times as large as its supplement.