Draw a line parallel to AB and DC . Using the Basic Proportionality Theorem and the constructed triangles inside the trapezium prove the required answer.
Complete step-by-step answer:
In trapezium ABCD with AB∥DC, drawing a line EF∥CD
Now according to Basic Proportionality Theorem which states that "If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".
Now in △ADC,
Since EO∥CD ( from construction )
⇒AEED=AOOC ( By Basic Proportionality Theorem ) (i)
Also in △ADB
⇒AEED=BOOD ( By Basic Proportionality Theorem ) (ii)
Now comparing equations (i) and (ii)
AOOC=BOOD
⇒AOBO=COOD ( cross multiplying )
Hence proved.
Note: Recall Basic Proportionality Theorem to solve such types of questions. Construction becomes important in solving such questions in a simple manner. We should make constructions wherever required.
