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Question

Question 9
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AOBO=CODO.

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Solution


Given, ABCD is a trapezium in which AB || DC in which diagonals AC and BD intersect each other at O.
To Prove that AOBO=CODO
Construction: Through O, draw EO || DC || AB
Proof
In ΔADC, we have OE || DC (By Construction)
AEED=AOCO...(i) [By using Basic Proportionality Theorem]
In ΔABD, we have OE || AB (By Construction)
AEED=BODO...(ii) [By using Basic Proportionality Theorem]
From equation (i) and (ii), we get
AOCO=BODO
AOBO=CODO


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