Question

Given ABC is right isosceles, X is the midpoint of AC.AB is congruent with BC.Prove AXB is isosceles.

Answer 1

We have to prove that the triangle AXB is isosceles.

We know that X is the midpoint of AC, and AB=BC.

As BC=AB, the measures of the angles A and C are equal, with a value of 45 degrees.

The segement XB divides the angle B in two equal parts, of 45 degrees each one.

Then, the triangle AXB has a right angle at point X, and two angles, at A and B, with measure of 45 degrees. Then, the sides AX and BX have to be equal.

If both sides have equal length, then the triangle AXB has two equal sides and is isosceles.