Question

If fig DE ll QO and DE ll OR show that EF llQR

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Answer 1

Step-by-step explanation:

if DF ll Send me a copy of nodal spaces in this emai is not available until the answer is

Answer 2

Aɴsᴡᴇʀs:- First use the basic proportionality theorem in ∆POQ & ∆POR and equate them , then apply Converse of basic proportionality theorem in ∆ PQR to prove required result..

Basic proportionality theorem (BPT):

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio.
This theorem is also known as Thales theorem.

Converse of basic proportionality theorem:

If a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.

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Sᴏʟᴜᴛɪᴏɴ:

In POQ, DE||OQ. ( given)

PE/EQ = PD /DO...............(i)
[ By BPT]

In ∆POR, DF||OR. (given)

PF/FR = PD/DO..................(ii)
[By BPT]

From eq i & eq ii 
PE/ EQ = PF/FR

In ∆ PQR we have

PE/ EQ = PF/FR

Hence, EF||QR 

[ By Converse of BPT]
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Hope this will help you.