Prove that the angles opposite to equal sides of an isosceles triangle

1.	Prove that the angles opposite to equal sides of an isosceles triangle are equal
Answer» Given: A triangle ABC in which AB = ACTo Prove: ∠ABC = ∠ACBConstruction: Draw the bisector AD of A so as to intersect BC at D.Proof: In ∆ADB and ∆ADC,AD = AD \| CommonAB = AC \| Given∠BAD = ∠CAD\| By Construction∴ ∆ADB ≅ ∆ADC \| SAS congruence rule∴ ∠ABD = ∠ACD \| CPCT⇒ ∠ABC = ∠ACB

Discussion