Question

Suppose triangle ABC is right isosceles. Vertex B is at (0, 0). Points A and C are at (0, 2a) and (2a, 0). X is the midpoint of AC. How can you tell that triangle AXB is isosceles?

Answer 1

X(a,a)
AX=BX
HENCE ISCOSCELES

Answer 2

you can show that: \[\large \triangle ABX \cong \triangle CBX\]