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