Angles opposite to two equal sides of a triangle are equal. GIVEN : ` A B C` in which `A B=A C` TO PROVE : `/_C=/_B` CONSTRUCTION : Draw the bisector `A D` of `/_A` which meets `B C` in `D` Figure

Explanation

In`triangleABC`, `AB=AC`
To prove: Angle opposite to `AB=`Angle opposite to `AC`
`∠C=∠B`
Construction: Draw `AD` perpendicular to `BC`
`∴∠ADB=∠ADC=90^@`
Proof: Consider `△ABD` and `△ACD`
`AD` is common
`AB=AC`
`∴∠ADB=∠ADC=90^@`
Hence` ∠ABD=∠ACD`
`∠ABC=∠ACB`
`∠B=∠C`
Hence proved
This is known as Isosceles triangle theorem.