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From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is midpoint of BC

Hence, $AL = 2 DC$ .Is the above statement true?

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True

False

answer is A.

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Detailed Solution

Given,
A parallelogram = ABCD
Midpoint of BC = E
Now,
In the triangle

△ CED

and

△ BEL

We have

∠ CED = ∠ BEL

(Angles which are vertical opposite)

EC = BE

(E = midpoint of BC)

∠ DCE = ∠ EBL

(Alternate Angles)
Thus,

the triangle

are congruent by side angle side rule of congruency,

△ CED ≅ △ BEL

So, by corresponding sides of congruent triangles,

CD = BL then

CD = AB

(ABCD is a parallelogram)
Thus, we have

CD = BL = AB

Now,

AL = AB + BL

AL = AB + AB

AL = 2 AB

AL = 2 CD

Hence, the given statement is true.
Correct option is 1.

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