Distance between Two Points on the Same Coordinate Axes
Question 9 AB...
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) ∴DEEA=DOBO...(ii) [By using Basic Proportionality Theorem] From equation (i) and (ii), we get AOCO=BODO ∴AOBO=CODO