Question

ΔABC is an isosceles triangle in which AB = AC. Show that ∠B = ∠C.

Answer 1

Given the ΔABC is an isosceles triangle and AB = AC

Let D be the mid point of BC; Join A to D.

Now in ΔABD and ΔACD

AB = AC (given)

BD = DC (construction)

AD = AD (common)

$\therefore$ ΔABD $\cong$ ΔACD (SSS congruence rule)

$\Rightarrow$ ∠B = ∠C (CPCT)