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Question

In trapezium ABCD, side ABCD and diagonals AC and BD intersect each other at O.
Prove that: OAOC=ODOB.

627019_1dac128c91a74533a75d023b0355e1b6.png

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Solution

In trapezium ABCD, side ABCD

Diagonals AC and BD intersect each other at point O.

To prove: OAOC=ODOB

Proof:

In AOB and COD

OAB=OCD ..........(Alternate angles)

and AOB=COD........(Vertically opposite angles)

Hence, AOBCOD .......(By AA test of similarity)

OAOC=ODOB........[C.S.S.T] [henceproved]

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