Question

Prove that the angle opposite to the equal sides of an equilateral
triangle are equal.​

Answer 1

Answer:

because all the sides of a equilateral triangle are same and the angle sum property of a triangle is 180° .so we can take 3x=180° and solve

Answer 2

The angle opposite to the equal sides an equilateral triangle are equal.

Step-by-step explanation:

Given Data

To prove that- the angle opposite to the equal sides an equilateral triangle are equal.

Let us consider an equilateral triangle ABC,

Where AB = AC

We have to prove that ∠B = ∠C

Drawn an intersecting line line which bisects BC at the point named D, at an angle of ∠A.

From the figure,

In Triangle BAD and triangle CAD

AB = AC

∠BAD = ∠CAD

Also, AD = AD from the above relation

By SAS Congruence rule,

Triangle ≅ Triangle CAD

Then , by Corresponding Points of Congruence triangle,

∠ABD = ∠ACD

Therefore, ∠B = ∠C

Therefore, the angle opposite to the equal sides of an equilateral triangle are equal.

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