Question

In $△ABC,AB=BC,AD\perp BC,CE\perp AB.$ Prove that $AD=CE$.

Answer 1

Given: In $△ABC,AB=BC,AD\perp BCAB\perp CE$

To prove $AB=CE$

We know that,

Area of triangle= $\frac{1}{2}\times Base\times Height$

So, $ar\left(△ABC\right)=\frac{1}{2}\times AD\times BC$

$ar\left(△ABC\right)=\frac{1}{2}\times CE\times AB$

As, both are equal,

$\frac{1}{2}\times AD\times BC=\frac{1}{2}\times CE\times AB$

$\because \frac{AB}{2}=\frac{BC}{2}$

Hence, $AD=CE$