Question

ABCD is a parallelogram. X, Y are mid points of AD and BC. Show that AP=PQ=QC.​

Answer 1

Answer:

AD = BC (Opposite sides of a parallelogram)

Therefore, DX = BY ( 1/2 AD = 1/2 BC)

Also, DX || BY (As AD || BC)

So, XBYD is a parallelogram (A pair of opposite sides equal and parallel)

i.e., PX || QD

Therefore, AP = PQ (From ∆AQD where X is mid-point of AD)

Similarly, from ∆CPB, CQ = PQ ---> (1)

Thus, AP = PQ = CQ [From (1) and (2)] ---> (2)