Question

Triangle ABC is a isosceles triangle in wch AB=AC. Side BA is produced to D such that AD=AB.show that angleBCD is a right angle

Answer 1

here is your answer
hope it help you

Answer 2

ΔABC is an isosceles triangle   (given)

so, AB = AC

$\bf \angle{ABC} = \angle{ACB}.......(i)$

$\bf AB = AC\\and\\AC = AD$

Now,

In ΔACD

$\bf \angle{CDA}=\angle{ACD}$

⇒ $\bf \angle{CDB}=\angle{ACD}......(ii)$

now,

$\bf \angle{ABC}+\angle{CDB}=\angle{ACB}+\angle{ACD}$

⇒ $\bf \angle{ABC}+\angle{CDB}=\angle{BCD}.......(iii)$

now,

In ΔBCD

$\bf \angle{BCD}+\angle{DBC}+\angle{CDB}=180^o$

⇒ $\bf \angle{BCD}+\angle{ABC}+\angle{CDB}=180^o$

⇒ $\bf \angle{BCD}+\angle{BCD}=180^o$     from eq.(iii)

⇒ $\bf 2\angle{BCD}=180^o$

⇒ $\bf \angle{BCD}=\frac{180}{2}$

⇒ $\bf \angle{BCD}=90^o$

∴ Hence,

$\bf \angle{BCD}\: \:is\: \:a\: \:right\:\: angle$