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.
