CONGRUENCE OF SIMPLE POLYGONS B7

Prove that the following triangle is isosceles.

Solution

Given: triangle EFG with F produced to H.

Required to prove: ∆EFG is isosceles

Proof: EH = HG (given)

<EHF = <GHF = 90⁰ (given)

FH = HF (common line)

∆EHF ≡ ∆GHF by SAS rule 

FE = FG (Equal corresponding sides)

Hence ∆EFG is isosceles (proved)