Question

ABCD is a trapezium in which AB||DC and its diognals intersect each other at the point O. Show that AO/BO = CO/DO.​

Answer 1

ABCD is a trapezium in which AB parallel to DC and its diagonals intersect each other at point O

ABCD is a trapezium in which AB||DC and its diagonals intersect each other at point 'O'.

Answer 2

Answer:

draw OE parallel AB. ( by construction)

AB parallel DC ( given).

in triangle ACB,

CO/OA= CE/ EB ( by B.P.T) ---------(1)

=now, in triangle CDB,

DO/OB=CE/EB -------------(2)

from (1) and (2)

we get CO/OA = DO/OB

cross multiplication

CO×OB =DO×OA

Co/DO=OA/OB

hence proved.

hope it helps you