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Angles Opposite to Equal Sides of a Triangle are Equal

Theorem: Angles opposite to equal sides of an isosceles triangle are equal.
Given:
ΔABC such that AB = AC
To Prove: ABC = ACB
Construction: Draw AD, the bisector of BAC to meet BC at D.

Proof: In Δ ADB and Δ ADC,
         AB = AC ... (Given)
         AD = AD ... (Common)
       BAD = CAD ... (by construction)
Δ ABD
Δ ACD ... (SAS Cong. Axiom)
ABD = ACD    (CPCT)

ABC = ACB

 





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