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Q.

State whether the given statement is True or False.


Statement: Through the midpoint M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC at L and AD produced at E. Then EL = 2BL.


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a

True

b

False 

answer is A.

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Detailed Solution

ABCD is a parallelogram. M is the midpoint of CD.
4455.jfifIn ΔBCM and ΔEDM
CM = DM (M is midpoint of CD)
∠BMC = ∠DME (Vertical opposite)
∠BCM = ∠EDM (alternate interior angles)
∴ ΔBCM ≅ ΔEDM (ASA congruence)
⇒ BC = DE (by CPCT)
Also, BC = AD (opposite side of a ||gm ABCD)
Adding above two equations we have,
BC + BC = AD + DE
⇒ 2BC = AE ..............(i) Now, in Δ BLC and Δ ALE, we have
∠EAL = ∠BCL (∴alternate angles)
∠BCL = ∠AEL(∴alternate angles)
∴ ΔBCL ∼ ΔELA
⇒ BLEL = BCAE 
⇒ BLEL = BC2BC 
⇒ BLEL = 12 
⇒ EL = 2BL
Therefore it is true that EL = 2BL.
So, option (1) is correct.
 
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