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INDIRECT PROOF Given: ABC is a right triangle Prove: ABC has no obtuse angles 1. Assume ABC ahs an obtuse triangle and that angle B is obtuse 2. < A + <C = 90 <A = 90 - <C <A > 90 90- <C >90 <C < 0 3. However we cant have 0 degrees A C B Given: DEF is an obtuse triangle Prove: a triangle cannot have two obtuse angles 1. <D >90 <E > 90 <D+ <E + <F = 180 90+90+<F = 180 <F= 0 2. No angles can be 0 D E F Given: supplementary angles Prove: they cant have both obtuse angles 1. Assume that the two supplementary angles are obtuse angles 2. A>90 B>90 <A + <B > 180 3. They are not supplementary angles, therefo re they cant be obtuse angles