Question

$△ABC$ is an isosceles triangle with $AB=AC$. Draw $AP\perp BC$ to show that $\angle B=\angle C.$

Answer 1

Showing that $\angle B=\angle C.$

Given:

In $∆ABC,$

$AB=BC$

$AP\perp BC$

To Prove:

$\angle B=\angle C$

Proof

In $∆APB$ and $∆APC$

$\angle APB=\angle APC$—————[ each $90°$]

$AB=AC$ ——————-[given]

$AP=AP$ ——————–[common]

$\therefore ∆APB\cong ∆APC$ ———-[R.H.S congruence rule]

$\angle B=\angle C$ —————[ by C.P.C.T]

Hence we proved that $\angle B=\angle C$