# Write an indirect proof: An isosceles triangle cannot have an obtuse base angle.

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### 1 Answer

In an indirect proof you assume that the conclusion is false, and then attempt to arrive at a logical inconsistency thus showing that your assumption was wrong.

This uses the contrapositive: If p=>q then ~q => ~p; the two statements are logically equivalent.

Prove that an isosceles triangle cannot have an obtuse base angle:

Assume that there exists an isosceles triangle with an obtuse base angle. Since the triangle is isosceles, the base angles are congruent. Then two angles of the triangle have measure greater than 90 degrees. Regardless of the size of the vertex angle, the sum of the angles of this triangle is greater than 180 degrees. But this is impossible in Euclidean geometry.

Therefore the initial assumption, that an isosceles triangle has an obtuse base angle, must be false.