Question

In triangle ABC, $AB=AC$; $BE$ $\perp$ $AC$ and $CF$ $\perp$ $AB$.

State whether following statement is true or false

$AF=AE$

• A. True
• B. False

Answer 1

The correct option is A True

In $△BFC$ and $△BEC$,
$BC=BC$ (Common)
$\angle FCB=\angle EBC$ (Given, AB = AC)
$\angle BFC=\angle BEC$ (each ${90}^{\circ }$)
Thus, $△BFC\cong △CEB$ (ASA rule)
Hence, $BF=CE$ (By cpct)
$AB=AC$ (Given)
Hence, $AB-BF=AC-CE$
$AF=AE$