Question

b) In the figure, ABCD is a parallelogram. E and F are the mid-points of sides AB and CD
respectively. PO is any line that meets AD, EF and BC in points P, and respectively. Prove
that PO = 0Q
​

Answer 1

Answer:

Answer

Since E and F are mid-points AB and CD respectively.

∴AE=BE= 21

AB and CF=DF= 21 CD

But, AB=CD

∴ 21

AB= 21

CD⇒BE=CF

Also, BE∥CF [∵AB∥CD]

∴ BEFC is a parallelogram.

⇒BC∥EF and BE=PH ...(i)

Now, BC∥EF

⇒AD∥EF [∵BC∥AD as ABCD is a ∥ gm }

⇒AEFD is a parallelogram

⇒AE=GP ...(ii)

But, E is the mid-point of AB.

∴AE=BE

⇒GP=PH [Using (i) and (ii)]

Step-by-step explanation:

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