ABCD is a parallelogram, E and F are the mid-points of AB and CD respectively. GH is any line intersecting AD,EF and BC at G, P and H respectively. Prove that GP=PH.

Question

Philoid · Accepted Answer

Since E and F are mid points of AB and CD

∴ AE = BE =

And CF = DF =

∵ AB = CD

∴

= BE = CF

∴ BEFC is a parallelogram

= BE││EF and BF= PH---------------(i)

Now, BC││EF

=AD││EF ∵ BC││AD as ABCD is a parallelogram

= AEFD is a parallelogram

= AE = GP

But is the mid point of AB

∴ AE=BE

= GP=PH proved