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Question
In ∆ABC, D and E are points on sides AB and AC respectively such that AD ✕ EC = AE ✕ DB. Prove that DE || BC.
Solution
Given: In Δ ABC, D and E are points on sides AB and AC such that `ADxxECxxAExxDB`
To Prove: DE||BC
Proof:
Since `ADxxECxxAExxDB`
`⇒ (DB)/(AD)=(EC)/(AE)`
`⇒ (DB)/(AD)+1=(EC)/(AE)+1`
`⇒ (DB+AD)/(AD)=(EC+AE)/(AE)`
`⇒ (AB)/(AD)=(AC)/(AE)`
∴ DE || BC (Converse of basic proportionality theorem)
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