Question

Prove that base angle of an isoceles triangle are equal

Answer 1

Theorem 1: Angles opposite to the equal sides of an isosceles triangle are also equal.

Proof: Consider an isosceles triangle ABC where AC = BC.

We need to prove that the angles opposite to the sides AC and BC are equal, that is, ∠CAB = ∠CBA.

Isosceles Triangle

We first draw a bisector of ∠ACB and name it as CD.

Now in ∆ACD and ∆BCD we have,

AC = BC (Given)

∠ACD = ∠BCD (By construction)

CD = CD (Common to both)

Thus, ∆ACD ≅∆BCD (By SAS congruence criterion)

So, ∠CAB = ∠CBA (By CPCT)

Hence proved.

Answer 2

Step-by-step explanation:

angles opposite to equal sides are equal is a theorem in isosceles triangles and sides opposite to equal angles are equal