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Question

ABCD is a trapezium in which AB parallel DCand its diagonals intersect each other at point O . show that AOBO=CODO


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Solution

Step-1 Construction:

Draw a line EF passing through O and also parallel to AB

Now,

ABllCD

EFllAB by Construction

EFllCD

Step-2 Basic Proportionality theorem:

Consider the ΔADC

Where EOllAB

According to the basic proportionality theorem

AEED=AOOC …………………(i)

Now consider ΔABD

where EOllAB

According to the basic proportionality theorem

DEEA=DOBO…………….(ii)

From equation (i) and (ii), we get,

AOOC=BODO

AOBO=CODO

Hence, proved.

Therefore we proved that AOBO=CODO


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