Question

Q3. The diagonals AC and BD of a parallelogram ABCD intersect at O. If P is the midpoint of AD, prove that

a) PQ || A B
b) PO=1/2 CD.

Answer 1

Explanation:

a) To prove that PQ || AB, we can use the fact that in any parallelogram, the opposite sides are parallel and equal. Therefore, since AD is parallel to AB, the line PQ which connects the midpoint of AD to the opposite corner A will also be parallel to AB.

b) To prove that PO = 1/2 CD, we can use the fact that in any parallelogram, the diagonals bisect each other. Therefore, since AC and BD intersect at O, PO must be equal to 1/2 of its length. Since the length of CD is twice that of PO, it follows that PO = 1/2 CD.