Question

Question 5 In the following figure, DE || OQ and DF || OR, show that EF || QR.

Class 10 - Math - Triangles Page 129

Answer 1

∆PQR s ED || QO

.°. PD/DO = PE/EQ ( from formula )-------(1)

∆POR s DF || OR

.°. PD/DO = PF/FR ( from formula )........(2)

from (1) and (2) we get

PE/EQ = PF/FR

.°. EF || QR

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Answer 2

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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Solution:

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.....