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Diagonals of a Parallelogram

In the given ...

Question

In the given figure, ABCP is a parallelogram and P is the mid point of CD. Then find which of the following option is correct?

$O A = \frac{1}{2} C D$

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$P D = A P$

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$A P = \frac{1}{2} B C$

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$O B = \frac{1}{2} B D$

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Solution

The correct option is D
$O B = \frac{1}{2} B D$

ABCP is a parallelogram with OP || BC.
Since P is the mid point of CD and OP || BC, O is the mid point of BD by converse of mid point theorem.

Therefore, $O B = \frac{1}{2} B D$

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In the given figure, ABCP is a parallelogram and P is the mid point of CD. Then find which of the following option is correct?

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In the given figure, ABCP is a parallelogram and P is the mid point of CD. Then find which of the following option is correct?

The correct option is D OB=12BD ABCP is a parallelogram with OP || BC. Since P is the mid point of CD and OP || BC, O is the mid point of BD by converse of mid point theorem. Therefore, OB=12BD

The correct option is D
$O B = \frac{1}{2} B D$

ABCP is a parallelogram with OP || BC.
Since P is the mid point of CD and OP || BC, O is the mid point of BD by converse of mid point theorem.

Therefore, $O B = \frac{1}{2} B D$