Question

Question 11
In the following figure, E is a point on side CB produced, of an isosceles triangle ABC, with AB = AC. If AD $\perp$ BC and EF $\perp$ AC, prove that $\Delta ABD\sim \Delta ECF$.

Answer 1

It is given that ABC is an isosceles triangle.
$\therefore AB=AC$
$\Rightarrow \angle ABD=\angle ECF$........(i)
In $\Delta ABDand\Delta ECF$,
$\angle ADB=\angle EFC\left(Each{90}^{\circ }\right)$
$\angle ABD=\angle ECF$ (from (i))
$\therefore \Delta ABD\sim \Delta ECF$ (By using AAA similarity criterion)