Question

In triangle ABC; $AB=AC$, $BD\perp AC$ and $CF\perp AB$.
then $BA=CF$.
If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

Given: AB = AC
Thus, $\angle ABC=\angle ACB$ (Isosceles triangle property)..(I)
In $△BCD$ and $△BCF$,
$\angle ACB=\angle ABC$ (From I)
$BC=BC$ (Common)
$\angle BDC=\angle CFB$ (Each ${90}^{\circ }$)
Thus, $△BCD\cong △CBF$ (ASA rule)
Thus, $BD=CF$ (Corresponding sides)