Question

To
Quadrilateral ABCD, AD||DC the diagonal AC and DC intersect at point O. If AO = 2CO, BO = 2DO.show that AB= 2CD​

Answer 1

Hello dear ,

________________________

Given, a quadrilateral ABCD in which the diagonals AC and BD intersect each other at point O.

i)

It is given that, AO = 2 CO and BO = 2 DO

=> AO/CO = 2/1 and. BO/DO = 2/1

=> AO/CO = BO/DO = 2/1 - - - - - - - - - - - (1)

Now, in triangle AOB and triangle COD, we have

AO/CO = BO/DO [from (1)]

Also, ∠AOB = ∠COD [vertically opposite angles]

⇒ ΔAOB ~ ΔCOD [SAS similarity]

●●●●●●●●●●●●●●●●●●●●●●●

ii)

From (1), we have

AO/CO = BO/DO

On cross multiplication, we get

OA × OD = OB × OC

[Hence proved]

________________________

HOPE IT HELPS U !!!

Follow for more solutions...