Isosceles Triangle Theorem

This theorem states that a triangle is isosceles if and only if the sum of the squares of its two shorter sides is equal to the square of its longest side.

Problem

Given a triangle with sides of lengths a, b, and c, prove that the triangle is isosceles if and only if a^2 + b^2 = c^2.

Solution

by elrichendelgart 
A triangle is isosceles if and only if two of its sides have the same length. In other words, if a=b or b=c or a=c. This is also true if you take the lengths of the sides to be a^2, b^2, and c^2. So a^2 + b^2 = c^2 if and only if the triangle is isosceles.
A.I. Evaluation of the Solution

This solution is correct.

Evaluated at: 2022-11-12 04:16:38