Question

the diagonals AC and BD of a parallelogram ABCD intersect at O if P is the midpoint of a d prove that PO =1/2CD

Answer 1

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Answer 2

PO =1/2CD

Proved below.  

Step-by-step explanation:

Given:

Since ABCD is  a ∥gm , the two diagonals  bisect each other. So O is the mid point of AC.

A shown in the figure given below, In triangle ABD, P is the mid point of AD and O is the mid point of BD.

So, OP∥AB (mid point theorem)

Also, $OP=\frac{AB}{2}$

Since AB=CD

Hence  $OP=\frac{CD}{2}$