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Q.

Through M the mid-point of side CD of a parallelogram ABCD, the line BM is drawn intersecting AC at L and AD produced at E. State if “EL=2BL” is true or false.

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a

False

b

True

answer is B.

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Detailed Solution

It is given that that M is the mid-point of side CD of parallelogram ABCD.
Let us draw the figure according to the given data.
Question Image

Question Image

Δ B C M ~ Δ E D M M D = C M B C = D E A D = B C

A E = 2 B C Δ A C L ~ Δ A E L

Applying Thales theorem,

E L B L = A E B C = 2

E L = 2 B L

Hence,

E L = 2 B L

proved.
The given statement is true.
Hence, the correct option is 2.

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Through M the mid-point of side CD of a parallelogram ABCD, the line BM is drawn intersecting AC at L and AD produced at E. State if “EL=2BL” is true or false.