ABCD is a trapezium in which AB∥DC and its diagonals intersect each other at the point O. Show that AOBO=CODO .

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.