Question

In the given figure, if $\angle x=\angle y$ and AB = CB, then AE is _____.

• A. less than CD
• B. greater than CD
• C. equal to CD
• D. data insufficient

Answer 1

The correct option is C equal to CD

Consider $\Delta ABE$ and $\Delta CBD$.
Given, $\angle x=\angle y$.
$⟹$ ${180}^{\circ }-\angle x={180}^{\circ }-\angle y$
$⟹\angle CDB=\angle AEB$
Now, AB = CB (given) and
$\angle CBD=\angle ABE$ $(\because$ common angles in $\Delta ABE$ and $\Delta CBD$)
Hence, $\Delta ABE\cong \Delta CBD$
(by AAS criteria of congruency for triangles)
$\therefore$ AE = CD (CPCT)