Question

ABCD is a trapezium in which ab parallel DC and DC is equal to 30 cm and a b is equal to 50 cm if x and y are respectively the midpoints of AC and BC prove that area of DC y x is equal to 7 by 9 area of xy BA

Answer 1

Given: ABCD is a trapezium with AB || DC.Construction: Join DY and produce it to meet AB produced at P.
In triangle BYP and triangle CYD∠BYD = ∠CYD (vertically opposite angles)∠DCY = ∠PBY (alternate opposite angles as DC || AP and BC is the transversal)
and BY = CY (Y is the mid point of BC)
Thus △ BYP ≅ △CYD (By ASA congruence criterion)
DY = YP and DC = BPY is the id point of AD
XY || AP and XY = 1/2 AP (mid point theorem)XY = 1/2AP = 1/2(AB + BP) = 1/2 (AB + DC) = 1/2(50 + 30) = 1/2 x 80 = 40 cm
Since X and Y are mid points of AD and BC respectively.trapezium DCYX and ABYX are of same height say h cm.
Now area of DCYX / Area of ABYX = 1/2 (DC + XY)x h / 1/2 ((AB x XY)H = 30+ 40 / 50 + 40 = 70 / 90 = 7/ 99 ar (DCXY) = 7 ar (XYBA)

Answer 2

Answer:

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