Question

In the given figure, if x=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 $\Delta CBD$ for congruency
Here, $\angle x=\angle y$
So, ${180}^{\circ }-\angle x={180}^{\circ }-\angle y$
$\therefore \angle AEB=\angle CDB$
AB = CB (Given)
$\angle CBD=\angle ABE$ $(\because commonangleof\Delta ABEand\Delta CBD)$
So, $\Delta ABE\cong \Delta CBD$ (by A.A.S. as the common side is not included in between the equal angles)
Therefore, AE = CD (CPCT).