Q8 of 76 Page 10

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

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,


Hence, proved


More from this chapter

All 76 →
6

P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that the triangle BPQ is isosceles.

 7

Prove that each angle of an equilateral triangle is 60°.

 9

ABC is a triangle in which ∠B=2∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD. Prove that ∠BAC = 72°.

 10

ABC is a right angled triangle in which ∠A=90° and AB=AC. Find ∠B and ∠C.