Question

The figure below shows a trapezoid, ABCD, having side AB parallel to side DC. The diagonals AC and BD intersect at point O.

Answer 1

Answer:

Length of BO is three times the length of DO.

Step-by-step explanation:

In trapezoid ABCD, $CD\ ||\ AB$

In ΔCDO and ΔABO,

1. $m\angle CDO=m\angle ABO$ (Alternate interior angles)
2. $m\angle DCO=m\angle BAO$ (Alternate interior angles)

So, $\Delta CDO\sim \Delta ABO$ according to Angle-Angle similarity.

Therefore, the ratio of corresponding sides will be same.

$\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{OA}$

$\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{3\cdot OC}$

$\Rightarrow \dfrac{OD}{OB}=\dfrac{1}{3}$

$\Rightarrow OB=3\cdot OD$

Answer 2

BO is the same length as AO, and DO is the same length as CO. therefore BO is three times the length of DO.