ABCD is a parallelogram prove that DP by PQ is equal to DC by BQ and DQ by DP is equal to AQ by DC

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Kindly check the question you have posted. It is certain that the details about the points P and Q is missing. If you have referred this question from elsewhere either please check again or if it is the same you have an incomplete question.
So I would recommend you to close this post as satisfied and try to post the question in another session with complete information.
With the given information its unable to solve the question.

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Similar questions

Q. In figure,

A B C D

is a parallelogram
Prove that

\frac{D Q}{D P} = \frac{A Q}{D C}

Q. In figure,

A B C D

is a parallelogram
Prove that

\frac{D P}{P Q} = \frac{D C}{B Q}

Q. ABCD is a parallelogram, P is a point on side BC such that DP produced meets AB produced at L.. Prove that

(i)

\frac{D P}{P L} = \frac{D C}{B L}

(ii)

\frac{D L}{D P} = \frac{A L}{D C}

$P$ is a point on side $B C$ of a parallelogram $A B C D$ . If $D P$ produced meets $A B$ produced at point $L$ , prove that :
(i) $D P : P L = D C : B L$ .
(ii) $D L : D P = A L : D C$ .

ABCD is a parallelogram and APQ is a straight line meeting BC at Pend DC produced at Q. prove that the rectangle obtained by BP and DQ is equal to the rectangle contained by AB and BC.

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