Question

Abcd is a trapezium in which ab parallel to dc and its diagonals intersect each other at point o show that ao upon b is equals to c upon duo

Answer 1

Answer:

given-

AB ll CD

T.P- AO/BO= CO/DO

In ∆ AOB and ∆ COD

angle AOB = angle COD (V.O.A)

angle ABO = angle ODC (Alternate angle)

By AA similarity criterion

∆AOB ~ ∆COD

So, AO/CO = BO/DO = AB/CD ( By thales theorem)

Therefore, AO/CO=BO/DO

That is,AO/BO = CO/ DO

Hence proved.