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In the given figure, M is the mid-point of the side CD of parallelogram ABCD. BM when joined meets AC in L and AD produced in E. State if the given statement is true or false. “EL = 2BL”.

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True

False

answer is A.

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Detailed Solution

It is given that M is the mid-point of the side CD of parallelogram ABCD.
It is also given that when the line BM is extrapolated it meets the side AC in L and AD in E.
Let us draw the figure.
Question Image

We can write that in ΔBCM and ΔEDM,

M D = C M B C = D E

ΔBCM~ΔEDM (SS similarity criterion)
Similarly, for ΔBCL and ΔAEL,
∠EAL=∠BCL
∠ALE=∠BLC

Δ B C L ~ Δ A E L

(AA similarity)
Using the similar triangle’s property proportional side property, we can write that,

E L B L = A E B C = 2

E L = 2 B L

Hence,

E L = 2 B L

proved.
Therefore, the given statement is true i.e.,

.
Hence, the correct option is 1.

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