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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.

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Presentation on theme: "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."— Presentation transcript:

1 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 90 90- 90 <C < 0 3. However we cant have 0 degrees A BC

2 Given: DEF is an obtuse triangle Prove: a triangle cannot have two obtuse angles 1. 90 90 <D+ <E + <F = 180 90+90+<F = 180 <F= 0 2. No angles can be 0 D E F

3 Given: supplementary angles Prove: they cant have both obtuse angles 1. Assume that the two supplementary angles a re obtuse angles 2. A>90 B>90 180 3. They are not supplementary angles, therefor e they cant be obtuse angles

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