Q. 34.1( 246 Votes )

Answer :

Given: LM ll CB and LN ll CD

From the given figure:

In ΔALM and ΔABC

LM || CB**Proportionality theorem**: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion

Now, using basic proportionality theorem that the corresponding sides will have same proportional lengths, we get:

(i)

And in ΔALN and ΔACD corresponding sides will be proportional

Therefore,

(ii)

From (i) and (ii), we obtain

Hence, Proved.

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PREVIOUSE and F are points on the sides PQ and PR respectively of a Δ PQR. For each of the following cases, state whether EF || QR :(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cmNEXTIn Fig. 6.19, DE || AC and DF || AE. Prove that

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