Question

14. In a parallelogram ABCD, AC and
BD are its diagonal and intersect at
0. Pis mid-point of DO and Q is
mid point of OB (Fig. 19). Prove that
APCQ is a parallelogram.

pls explain or whose no the answer don't reply​

Answer 1

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Consider the diagram given in the question.

As we know, the diagonals of a parallelogram bisect each other. Therefore,

⇒AC and BD bisect each other at point O.

Thus,

⇒OA=OC and OB=OD

Now, consider points P and Q.

⇒BP=PQ=DQ ...... (1)

Now, since OB=OD, so

PB+OP=OQ+DQ

From equation (1),

DQ+OP=OQ+DQ

∴OP=OQ

Thus, AC and PQ bisects each other.

Thus, APCQ is a parallelogram, because both the diagonals bisect each other. Also, since, CQ and AP are the opposite sides of the parallelogram APCQ, they are parallel to each other.