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Geometry 2.7 – Prove Angle Pair Relationships Learning Target: By the end of today’s lesson we will be able to successfully prove angle pair relationships. RIGHT ANGLE THEOREM: All right angles are _________________________. CONGRUENT SUPPLEMENTS THEOREM: If two angles are supplementary to the same angle (or to congruent angles), then they are _________________. If l and 2 are supplementary and 3 and 2 are supplementary, then _______________. CONGRUENT COMPLEMENTS THEOREM: If two angles are complementary to the same angle (or to congruent angles), then they are ________________. If 4 and 5 are complementary and 6 and 5 are complementary, then _____________. LINEAR PAIR THEOREM: If two angles form a linear pair, then they are _____________________. l and 2 form a linear pair, so l and 2 are supplementary and m1 + m2 = ______. VERTICAL ANGLES THEOREM: Vertical Angles are ____________________. 1) Given: 1 and 2 are supplements. 1 and 4 are supplements. m2 = 45° Prove: m4 = 45° Statements: Reasons: 1) 1 and 2 are supplements 1) __________________________________________________ 1 and 4 are supplements 2) ____________________________________ 2) Congruent Supplements Theorem 3) m 2 = m 4 3) __________________________________________________ 4) m2 = 45° 4) __________________________________________________ 5) m4 = 45° 5) __________________________________________________ 2) Given: 4 is a right angle. Prove: 2 and 4 are supplementary. Statements: Reasons: 1) 4 is a right angle. 1) __________________________________________________ 2) ____________________________________ 2) Definition of a Right Angle 3) 2 4 3) __________________________________________________ 4) m2 + m4 = 180° 4) __________________________________________________ 5) 2 and 4 are supplementary 5) __________________________________________________ 3) Use the picture below to find the indicated angle. a) If m4 = 63°, find m1 = _________ and m2= ____________. b) If m3 = 121°, find m1= _______, m2=_______, and m4=_________. 4) Write and solve an equation to find x. Use x to find mAEB.