ABCD is a trapezium in which, AB  DC and DC = 40 cm and AB = 60 cm. If X and Y are, respectively, the mid points of AD and BC, prove that XY = 50 cm.

Asked by Topperlearning User | 17th Aug, 2017, 01:54: PM

Expert Answer:

Join DY and produce it to meet AB produced at P.
In BYP and CYD
BYP =CYD                     (vertically opposite angles)
DCY =PBY                     (alternate angles)
BY = CY                                 (given)
BYP  CYD                   (ASA)
DY = YP and DC = BP
  Y is the mid point of DP
Also, X is the mid point of AD
Hence XY = 50 cm.

Answered by  | 17th Aug, 2017, 03:54: PM