Question

In the given figure, if DE ll AQ and DF ll AR then prove that EF ll QR.

Answer 1

Hlo frnd..

As DE || AQ
Therefore, by converse of mud point theorem,
E and D are mkd points of PQ and PA respectively.


As DF || AR
Therefore, by converse of mid point theorem,
F and D are mid points of PR and PA respectively.

Now,In triangle PQR, E is mid point of PQ and F is mid point of PR. Therefore, by mid point theorem, EF || QR.

THNX...

Answer 2

Given :

DE || AQ And DF || AR .

Required :

To Prove EF || QR .

Consider ∆APQ

Here , ED || QA

Therefore , By Thales Theorem

PE / EQ = PD / DA => 1

Now , Consider ∆PAR

Here , DF || AR

Therefore , By Thales Theorem PD / PA = PF / FR => 2

From - 1 & 2 We Can See That

PE / EQ = PF / FR

Therefore By Converse Thales Theorem We Can See That EF || QR In ∆ PQR ( FE / EQ = PF / FR )

HENCE PROVED

Hope It Helps u

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