INDIRECT PROOF

Given: ABC is a right triangleProve: 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 < 03. However we cant have 0 degrees

A

BC

Given: DEF is an obtuse triangleProve: a triangle cannot have two obtuse angles1. <D >90 <E > 90 <D+ <E + <F = 180 90+90+<F = 180 <F= 0 2. No angles can be 0

D

EF

Given: supplementary anglesProve: they cant have both obtuse an-gles

1. Assume that the two supplementary angles are obtuse angles2. A>90 B>90 <A + <B > 1803. They are not supplementary angles, therefore they cant be obtuse angles