Question

How to prove that each angles of equilateral triangle is 60 degree?

Answer 1

Consider an equilateral triangle ABC. As it is equilateral, AB=AC=BC;
As AB=AC → ∠A=∠C (Angles opposite equal sides are equal)
similarly ∠B=∠C
Now, addition of three angles of triangle is 180°
∴ ∠A+∠B+∠C=180°
∴3∠A=180° (as ∠A=∠B=∠C)
∴∠A=60°
Similarly ∠B=∠C=60°

∴ each angle of equilateral triangle is 60°

Answer 2

Hi there!

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Given :

ΔABC be an equilateral triangle.

∴ AB = BC = AC ( All sides of equilateral Δ are equal)

To prove :

∠A = ∠B = ∠C = 60°

Proof :

AB = AC

⇒ ∠C = ∠B (∠s opposite to equal sides are equal)...... (i)

Also, AC = BC

⇒ ∠B = ∠A (∠s opposite to equal sides are equal)...... (ii)

From (i) and (ii),

∠A = ∠B = ∠C.......... (iii)

In ΔABC,

∠A + ∠B + ∠C = 180° (Angle sum property of Δ)

⇒ ∠A + ∠A + ∠A = 180° [From eqⁿ (iii)]

⇒ 3∠A = 180°

⇒ ∠A = 180 / 3

⇒ ∠A = 60°

∴ ∠A = ∠B = ∠C = 60°

Hence, it is proved.

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Thanks for the question!

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