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Transcript
GEOMETRY Congruent Supplements and Congruent Complements PROOF Notes/Practice GOAL: Be able to recognize complementary and supplementary angles as well as apply their theorems and use them in proof. Warm up: Fill the given information into the figure! C Given: BFC 2 x , CFD 3 y B D BF DF , BFA y, DFE 4 x Find: DFE A F mDFE __________ Proving a THEOREM: Ex 1: Given: EOA is supplementary with AOB EOA is supplementary with EOD Prove: AOB EOD STATEMENTS REASONS E GEOMETRY Congruent Supplements and Congruent Complements PROOF Notes/Practice CONGRUENT SUPPLEMENTS THEOREM: If _________ angles are ____________________________ to the same angle, then __________________ are ____________________. REASON IN PROOF: ______________________________________________________ Theorem that follows from above: If _____________ are _______________________ to _________________________ angles, then they are ______________________. REASON IN PROOF: ___________________________________________ Ex. 2 – You try!! Given: QS TR POA is a right angle Pr ove : QOA TOP STATEMENTS O REASONS CONGRUENT COMPLEMENTS THEOREM: If _________ angles are_______________________ to the same angle, then __________________ are ____________________. REASON IN PROOF: ______________________________________________________ GEOMETRY Congruent Supplements and Congruent Complements PROOF Notes/Practice Theorem that follows from above: If _____________ are _______________________ to _________________________ angles, then they are ______________________. REASON IN PROOF: ______________________________________________________ Ex 3: Given: 5 and 6 are supplementary 7 and 8 are supplementary R O 5 S 6 7 6 7 Prove: 5 8 Y STATEMENTS REASONS Ex 4: ALGEBRAICALLY USING; Solve for x and y. A D ( y x ) 2x B ( y x) C E 8