Question

Show that angles of equilateral triangle are each 60

Answer 1

Hola!!!


We know that all sides of an equilateral triangle are equal to one another.


Consider triangle ABC in which AB=BC=CD

Since angles opposite to equal sides are equal ,

angle B = angle C (AB = AC)---(1)
angle C = angle A (AB = BC)---(2)
angle B = angle A (AC = BC)---(3)

1, 2 , 3 ==》angle A = angle B = angle C---'(4)

<A+ <B+ <C = 180° (angle sum property)

(4)===》 3 <A = 180°

<A = 60 °

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Using (4) ...we get ,

<B = 60°

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<C = 60°

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PROVED

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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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