Question

Prove that angles opposite to equal side of an isosceles triangle are equal

Answer 1

hence angle in an isosceles triangle opposite to each other areequal

Answer 2

Given :-

• ∆ABC is an isosceles triangle
• AB = AC

To Prove :-

• ∠B = ∠C

Construction :-

• Draw the bisector of ∠A intersecting BC at D

Proof OR Explanation :-

As we know, In an isosceles triangle two sides are equal. So,

$\tt \bold { In \: \triangle \: ADB \: and \: \triangle \: ADC }$

$\implies \rm AB = AC \qquad \quad \qquad \bold{(Given)}$

$\implies \rm \angle BAD = \angle CAD \qquad \bold{(By \: Construction)}$

$\implies \rm AD = DA \qquad \qquad \quad \bold{(Common)}$

$\therefore \qquad \boxed { \rm \triangle ADB \cong \triangle ADC }$

$\therefore \qquad \boxed { \boxed { \rm \bold { \angle B = \angle C }}} \qquad \quad \bold {(C.P.C.T)}$

Hence, angles opposite to equal side of an isosceles triangle are equal.

@Agamsain