Question

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In an isosceles triangle triangle ABC AB = AC. . Show that angles opposite to the equal sides are equal with diagram

Answer 1

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

Answer 2

theroerm is proved .........