Question

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that $\frac{AO}{BO}=\frac{CO}{DO}$

Answer 1

Given: ABCD is a trapezium, where AB||DC and its diagonals intersect each other at the point O

**To Show: **$\frac{AO}{BO}=\frac{OC}{OD}$

Answer:

Draw a line EF through point O, such that EF || CD
In ∆ADC, EO || CD............(I)

By using the basic proportionality theorem, we obtain
$\frac{ED}{AE}=\frac{OD}{BO}$
⇒$\frac{AE}{ED}=\frac{BO}{OD}$.............(II)
$\frac{AO}{OC}=\frac{BO}{OD}$
⇒$\frac{AO}{BO}=\frac{OC}{OD}$

Hence Proved