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Let A B C be a triangle and D and E be t...

Let `A B C` be a triangle and `D and E` be two points on side `A B` such that `A D=B E`. If `DP || BC` and `EQ || AC ,` Then prove that `PQ || AB`.

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`DeltaABC` in which D and E are two points such that AD=BE.
Also DP||BC and EQ||AC.
To Prove : PQ||AB
Proof: In `DeltaABC`Since DP|| BC.
` (AB)/(EA) =(BQ)/(QC)`
In `DeltaABC` since EQ||AC
`(BE)/(EA) =(BQ)/(QC)`
Now, as AD=BE
AD+DE= BE+DE
AE=BD (adding DE on both sides)
AE=BD ....(4)
From (1) (2) (3) and (4)
`(AP)/(PC)= (BQ)/(QC)`
PQ||AB ( by the converse of B.P. theroem) Hence proved.
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