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. Can't be determined

Answer 1

The correct option is C

equal to CD

Consider $\Delta ABE$ and $\Delta CBD$.
Given, x = y.
$⟹{180}^{\circ }-x={180}^{\circ }-y$
$\therefore \angle CDB=\angle AEB$
AB = CB (Given)
$\angle CBD=\angle ABE$ $(\because \text{common angle of}\Delta ABE\text{and}\Delta CBD)$
So, $\Delta ABE\cong \Delta CBD$ (by A.A.S. congruence criterion)
$\therefore AE=CD$ (CPCT)