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



If the length of AO is three times the length of CO, the length of BO is


one-third the length of AC


one-third the length of AB


three times the length of DO


three times the length of DC

The figure below shows a trapezoid, ABCD, having side AB parallel to side DC. The diagonals AC and BD intersect at point O. If the length of AO is three times t class=

Verified Answer :

ThatOneOcelot

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

InesWalston

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.

\(\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{OA}\)

\(\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{3\cdot OC}\)

\(\Rightarrow \dfrac{OD}{OB}=\dfrac{1}{3}\)

\(\Rightarrow OB=3\cdot OD\)


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