Question

In an isosceles triangle $ABC$ with $AB=AC,D$ and $E$ are points on $BC$ such that $BE=CD.$ The value of $\frac{AD}{AE}$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A

1

In $△ABD$ and $△ACE,$

$AB=AC$ [given]

$\angle B=\angle C$ [angles opposite to equal sides]

$BE=CD$ [Given]

Subtracting $DE$ from both sides, we get

$BE-DE=CD-DE$

$BD=CE$

$\Rightarrow △ABD\cong △ACE$ [SAS congruency]

Therefore, $AD=AE$ [CPCTE]

$\Rightarrow \frac{AD}{AE}=1$