Question

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

(2 Marks)

Answer 1

In $\Delta AXCand\Delta AYB,wehave:AC=AB\left(Given\right)$
$AX=AY\left(Given\right)$
$\angle BAC=\angle CAB(Anglecommonto\Delta AXCand\Delta AYB$
(1 mark)
∴$\Delta AXC\cong \Delta AYB\left(SAScriterion\right)$
So, CX=BY (CPCT)
Hence, proved. (1 mark)