Given: In triangle ABC, <A=135 degrees. Prove: <B `!=` 45 degrees. (Write an indirect proof.) (An image is not given)  

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lfryerda eNotes educator| Certified Educator

To prove indirectly that in a triangle ABC, if angle `A=135` degrees, then angle `B\ne 45` degrees, we first assume the negative of what we are trying to prove, then find some form of contradiction.

Angle `A=135` , and let angle `B=45` degrees.

Now we know that the sum of the angles in a triangle must add up to 180 degrees, so this means that 

`A+B+C=180` now sub in the values

`135+45+C=180`   solve for C

`C=180-180 = 0`

But if `C=0` degrees, then the triangle ABC cannot exist, since all angles must be greater than 0 degrees.  We have a contradiction.  Therefore the assumption that `B=45` degrees is incorrect.

Angle `B ne 45` degrees.