Question

show that in isosceles triangle angle opposite to equal side are equal?​

Answer 1

Answer:

An angle opposite to equal sides of an isosceles triangle is equal.

Step-by-step explanation:

Given:

An Isosceles triangle ABC, where the length of side AB equals the length of side AC.

To prove : AB = AC

Construction:

Let us draw the bisector of ∠A

Proof:

Let D be the point of intersection of this bisector of ∠A and BC.

Therefore ,by construction ∠BAD = ∠CAD.

In ∆BAD and ∆DAC,

AB = AC (Given)

∠BAD = ∠CAD (By construction)

AD = AD (Common side of a  triangle)  

So, ∆BAD ≅ ∆CAD (By SAS rule)

So, ∠ABD = ∠ACD (CACT)

So, ∠B = ∠C

Hence, Proved that an angle opposite to equal sides of an isosceles triangle is equal.