Question

In quadrilateral ABCD, the diagonals AC and BD intersect each other at point O. If AO = 2CO and BO = 2DO; show that: ΔAOB is similar to ΔCOD.

Answer 1

Since AO = 2CO and BO = 2DO,

`(AO)/(CO) = 2/1 = (BO)/(DO)`

Also, ∠AOB = ∠DOC  ...(Vertically opposite angles)

So, ΔAOB ∼ ΔCOD  ...(SAS criterion for similarity)