Question

In ∆ABC, D and E are points on sides AB and AC respectively such that AD ✕ EC = AE ✕ DB. Prove that DE || BC.

Answer 1

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)