Question

In the figure, ABCP is a parallelogram and P is the midpoint of CD. Which of the following is correct?​

• A. $OA=\frac{1}{2}CD$
• B. $OB=\frac{1}{2}BD$
• C. $AP=\frac{1}{2}BC$
• D. $PD=AP$

Answer 1

The correct option is B $OB=\frac{1}{2}BD$

Given that,
ABCP is a parallelogram with OP || BC.

We know that,
If a line is drawn through the mid-point of a side of a triangle parallel to the second side, it will bisect the third side.

Since P is the mid-point of CD and OP || BC, O is the mid point of BD by converse of mid-point theorem.

Hence, $OB=\frac{1}{2}BD$