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The diagonals of a quadrilateral ABCD in...

The diagonals of a quadrilateral ABCD intersect each other at the point O such that `(A O)/(B O)=(C O)/(D O)`. Show that ABCD is a trapezium.

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To prove that quadrilateral ABCD is a trapezium given that the diagonals intersect at point O such that \(\frac{AO}{BO} = \frac{CO}{DO}\), we will follow these steps: ### Step 1: Understanding the Given Condition We are given that the diagonals AC and BD intersect at point O, and the ratio of the segments created by this intersection is equal. This means that the segments AO and BO are proportional to segments CO and DO. ### Step 2: Construct a Parallel Line To show that ABCD is a trapezium, we need to demonstrate that one pair of opposite sides is parallel. We will construct a line EF that is parallel to side CD and passes through point O. ...
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