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Points D and E are the midpoints of side AB and side AC of ∆ABC respectively. Point F is on ray ED such that ED = DF. Prove that AFBE is a parallelogram. For this example write ‘given’ and ‘to prove’ and complete the proof.

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Given: D and E are the midpoints of side AB and side AC respectively. 

ED = DF 

To prove: AFBE is a parallelogram. 

Proof: 

seg AB and seg EF are the diagonals of AFBE. 

seg AD ≅ seg DB [Given] 

seg DE ≅ seg DF [Given] 

∴ Diagonals of AFBE bisect each other. 

∴ AFBE is a parallelogram. [ By test of parallelogram]

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