Question

25. In the figure, L and M are the midpoints of the sides AB and
DC respectively of the parallelogram ABCD; AM and DL
intersect at P, and CL cuts BM at Q. Prove that PMQL is a
parallelogram.
M​

Answer 1

Hence Proved

Step-by-step explanation:

Given,

ABCD is a parallelogram.

⇒AB ║ CD and AD ║ BC.

and AB = CD and AD = BC [We know that in a parallelogram opposite sides are parallel and equal]

Also,$\frac{1}{2}AB = \frac{1}{2}CD$

             ⇒AL = CM

Since M is a mid point on line CD and L is a mid point lies on AB.

 ⇒AL ║CM

⇒ALMC is a parallelogram.

Similarly BLDM is also a parallelogram.

Since ALMC is a parallelogram

⇒AM = CL and AM ║ CL

Since P lies on AM and Q lies on LC

⇒PM ║ LQ

Since a pair of opposite sides is parallel.

⇒PMQL is a parallelogram.

Hence Proved