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Transcript
Complementary and Supplementary Angles Geometry – Notes Name: _____________________________ Period: _________ Goal: Be able to recognize complementary and supplementary angles and apply their theorems. Warm-up: Given: BFC 2x, CFD 3y BF DF, BFA y, DFE 4x Find: DFE _________________________ angles are 2 angles whose sum is ____________(a right angle.) Each of the two angles is the ____________________ of the other. __________________________ angles are 2 angles whose sum is ______________ (a straight angle.) Each of the 2 angles is the ____________________ of the other. Given: Diagram as shown. Prove: 1 is supplementary to 2 Statements Reasons Theorem – If two angles are __________________________and__________________________ then each angle is a ________________________. Congruent Supplements Theorem – If two angles are _______________________of the same ____________________angles, then the 2 angles are ________________________. Congruent Complements Theorem - If two angles are _______________________of the same ____________________angles, then the 2 angles are ________________________. Given: Diagram as shown. 6 7 Prove: 5 8 Statements Example: Solve for x and y. Reasons Example: One of two supplementary angle is four times the measure of the other. Find the measure of the supplement. Example: One of two complementary angles is three more than twice the other. Find the measure of the complement. Given: TVK is a right angle Prove: 1 is complementary to 2 Statements Reasons