Question

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which means DC at point O and BC produced at P . prove that :
(i) BP = 2AD
(ii) O is mid-point of AP​

Answer 1

Answer:

Given ABCD is parallelogram, so AD = BC, AB = CD.

Consider triangle APB, given EC, is parallel to AP and E is the midpoint of side AB.

So by midpoint theorem,

C has to be the midpoint of BP.

So BP = 2BC, but BC = AD as ABCD is a parallelogram.

Hence BP = 2AD

Consider triangle APB, AB || OC as ABCD is a parallelogram.

So by midpoint theorem,

O has to be the midpoint of AP.

Hence Proved.