ABCD is a trapezium in which AB||CD and AB=2CD.If its diagonals intersect each other at O, find ratio of areas of triangle AOB and triangle COD.

Asked by Barman.rachna | 27th Jun, 2019, 11:46: AM

Expert Answer:

Given that AB || CD and AB = 2CD
angle OAB = angle OCD            alternate angles
angle OBA = angle ODC            alternate angles
ΔAOB ~ ΔCOD                          AA similarity criterion
ar(ΔAOB)/ar(ΔCOD) = (AB/CD)2 = (2/1)2 = 4/1 i.e. 4:1.

Answered by Sneha shidid | 28th Jun, 2019, 09:54: AM