Angles A, B, C of a triangle ABC are equal to each other. Prove that �

1.	Angles A, B, C of a triangle ABC are equal to each other. Prove that Δ ABC is equilateral.
Answer» Given that A, B, C of a triangle ABC are equal to each other. We have to prove that, Δ ABC is equilateral. We have, ∠A = ∠B = ∠C Now, ∠A = ∠B BC = AC (Opposite sides to equal angles are equal) ∠B = ∠C AC = AB (Opposite sides to equal angles are equal) From the above, we get AB = BC = AC Therefore, ΔABC is an quadrilateral triangle. Hence, proved

Angles A, B, C of a triangle ABC are equal to each other. Prove that Δ ABC is equilateral.

Answer»

Given that

A, B, C of a triangle ABC are equal to each other.

We have to prove that,

Δ ABC is equilateral.

We have,

∠A = ∠B = ∠C

Now,

∠A = ∠B

BC = AC (Opposite sides to equal angles are equal)

∠B = ∠C

AC = AB (Opposite sides to equal angles are equal)

From the above, we get

AB = BC = AC

Therefore, ΔABC is an quadrilateral triangle.

Hence, proved