Question

In ΔABC, X and Y are two points on AB and AC such that AX = AY. If AB = AC, prove that CX = BY.

Answer 1

In ΔABC
AB = AC
AX = AY
⇒ BX = CY
In ΔBXC and ΔCYB
BX = CY
BC = BC
∠B = ∠C = C  ...(AB = AC and angles opposite to equal sides are equal)
Therefore, ΔBXC ≅ ΔCYB   ...(SAS criteria)
Hence, CX = BY.