Question

Suppose ABC is an equiangular triangle. Prove that it is equilateral.(You have seen earlier that an equilateral triangleis equiangular. Thus for triangles equiangularity is equivalent to equilaterality.)

Answer 1

Answer:

We know that,

Sides opposite equal angles are equal

Thus angle A = angle B

therefore, BC = AC

Similarly  angle B = angle C

therefore, AC = AB

From above information, it can be said that an equiangular triangle is an equilateral triangle

Step-by-step explanation:

Answer 2

Δ ABC is an equiangular triangle ( Given)

Now,

Let AD be the perpendicular from A on side BC

In Δ ABD and Δ ACD

∠ABD = ∠ACD (Since, ΔABC is equiangular)

AD = AD (Common side)

∠ADB = ∠ADC (AD is a perpendicular)

Thus, Δ ABD and Δ ACD are congruent to each other.

AB = AC (Corresponding parts of the congruent triangles)

BD = DC(Corresponding parts of the congruent triangles)

Since the triangle is equiangular and AB = AC , so

AB = AC = BC ( All sides being equal )

Hence the triangle is equilateral