Krishna
0

Step 1: Construct EF parallel to AB and CD

NOTE: EF || AB || CD

Step 2:  Apply the basic proportional theorem to triangle ACD and ACB

THEOREM:  If a line is drawn parallel to one side of a triangle to intersect

the other two sides in distinct points, then the other two sides are divided

in the same ratio.

EXAMPLE:  In ∆ACD, EO || CD

\frac{AO}{OC}=\frac{EA}{ED}...................(1)

In ∆ACB, EO || AB

\frac{DO}{OB}=\frac{ED}{EA}

Take the reciprocal on both sides

\frac{BO}{DO}=\frac{EA}{ED}  ........................(2)

Step 3: Prove the required ratio by using equation (1) and (2)

From equation (1) and (2) we can write

\frac{AO}{OC}=\frac{BO}{DO}

\frac{AO}{BO}=\frac{OC}{OD}

Hence proved