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.

Question

In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of &#x2206;ABC such that AX=AY. Prove that CX=BY.

Philoid · Accepted Answer

Here it is given that AX = AY.

Now in ∆CXA and ∆BYA,

AX = AY

∠XAC = ∠YAB … Same angle or common angle.

AC = AB … given condition Hence by SAS property of congruency,

∆CXA ≅ ∆BYA

Hence by cpct, we conclude that,

CX = BY