Question

In Fig. X and Y are two points on equal sides AB and AC of a ΔABC such that AX = AY. Prove that XC = YB. [2 MARKS]

Answer 1

Concept : 1 Mark
Proof : 1 Mark

In $\Delta$s AXC and AYB, we have

AX = AY [Given]
$\angle$A = $\angle$A [Common angle]
AC = AB [Given]

So,
$\Delta$AXC $\cong$ $\Delta$AYB [SAS congruence criterion]

$\Rightarrow$ XC = YB [Since corresponding parts of congruent triangles are equal]