Question

Prove that an equilateral triangle is equiangular.l​

Answer 1

$\underline{\huge\mathfrak{Answer:}}$

Please refer to the attachment provided above for the figure :)

Let , ABC is an equilateral triangle .

Therefore ,

AB = BC = AC .

We have to prove that ,

angle A = angle B = angle C

Proof :-

Since , AB = AC

Therefore ,

angle B = angle C ..... (1) (Opposite angles of equal sides of a triangle)

Again since , AC = BC

Therefore ,

angle A = angle B ..... (2) (Opposite angles of equal sides of a triangle)

Lastly since , BC = AB

Therefore ,

angle A = angle C ..... (3) (Opposite angles of equal sides of a triangle)

Now , from equations (1) , (2) and (3) , we have :-

angle A = angle B = angle C .

Hence proved ! :)

Let , angle A = angle B = angle C = x (let)

Here , since all the angles are equal , therefore measure of the angles will be :-

x + x + x = 180°( Sum of all the angles of a triangle is 180°)

=> 3x = 180°

=> x = 60°