Question

In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of △ ABC such that AX = AY. Prove that CX = BY.

Answer 1

It is given that AX = AY

Considering △ AXC and △ AYB

∠ A is common i.e. ∠ A = ∠ A

We know that the sides of equilateral triangle are equal so we get

AC = AB

By SAS congruence criterion

△ AXC ≅ △ AYB

XC = YB (c. p. c. t)

Therefore, it is proved that CX = BY.