Q : 4 In Fig. , ABCD is a parallelogram and BC is produced to a point Q such that . If AQ intersects DC at P, show that .
[Hint : Join AC.]
ABCD is a ||gm and AD = CQ. Join AC.
Since DQC and ACD lie on the same base QC and between same parallels AD and QC.
Therefore, ar(DQC) = ar(ACD).......(i)
Subtracting ar(PQC) from both sides in eq (i), we get
ar(DPQ) = ar(PAC).............(i)
Since PAC and PBC are on the same base PC and between same parallel PC and AB.
Therefore, ar(PAC) = ar(PBC)..............(iii)
From equation (ii) and eq (ii), we get