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Question -

P and Q are the points of trisection of the diagonal BD of a parallelogram ABCD. Prove that CQ is parallel to AP. Prove also that AC bisects PQ.



Answer -

Figure can be drawn as follows:
┬а
We have P and Q as the points of trisection of the diagonal BD of parallelogram ABCD.
We need to prove that AC bisects PQ. That is,┬а┬а.
Since diagonals of a parallelogram bisect each other.
Therefore, we get:
┬а┬аand┬а┬а┬а
P and Q as the points of trisection of the diagonal BD.
Therefore,
┬а┬аand┬а┬а
Now,┬а┬а┬аand┬а┬а
Thus,
┬а
┬а
AC bisects PQ.
Hence proved.

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