#### notes

Construct a triangle in which two sides are equal, say each equal to 3.5 cm and the third side equal to 5 cm in following fig.

A triangle in which two sides are equal is called an isosceles triangle. So, ∆ ABC of above Fig. is an isosceles triangle with AB = AC.

#### theorem

**Theorem :** Angles opposite to equal sides of an isosceles triangle are equal. **Proof :** We are given an isosceles triangle ABC in which AB = AC. We need to prove that ∠ B = ∠ C. Let us draw the bisector of ∠ A and let D be the point of intersection of this bisector of

∠ A and BC in following fig.

In ∆ BAD and ∆ CAD,

AB = AC (Given)

∠ BAD = ∠ CAD (By construction)

AD = AD (Common)

So, ∆ BAD ≅ ∆ CAD (By SAS rule)

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

So, ∠ B = ∠ C

**Theorem :** The sides opposite to equal angles of a triangle are equal.

This is converse of above theorem.