Question

4. Prove logically that angles opposite to equal sides of an isosceles triangle are equal in measure.​

Answer 1

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

Given, an Isosceles triangle ABC, where the length of side AB equals the length of side AC.Therefore, AB = AC

Construction:

1. Let us draw the bisector of ∠A

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

:. By construction, ∠BAD = ∠CAD.

• In ∆BAD and ∆DAC,

AB = AC (Given)

∠BAD = ∠CAD (By construction)

AD = AD (Common side in both triangle) 

So, ∆BAD ≅ ∆CAD (By SAS rule)

So, ∠ABD = ∠ACD, since they are corresponding angles of congruent triangles.

So, ∠B = ∠C

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