Question

If two angles of a triangle are equal then the sides opposite to them are also equal prove this statement.​

Answer 1

Answer

Given:-

Two angles of a triangle are equal.

To Prove:

Sides opposite to equal angles are also equal.

Construction:

Draw OD , the bisector of ∠A meeting MG at D.

Solution: Let OMG be a triangle in which

∠M = ∠G

OM = OG {to prove}

In ∆OMD and ∆OGD we have

➮ ∠M = ∠G (given)

➮ ∠MOD = ∠GOD (by construction)

➮ OD = OD (common in both ∆s)

∴ ∆OMD = ∆OGD (by Angle Angle Side criteria)

Hence,

By OM = OG (by CPCT)

$\large\bold{\texttt {Proved }}$

★ See this

If two opposite angles of a triangle are equal then the side opposite to these angles are also equal. This is a property of isosceles triangle.