Question

ABCD is a trapesium in which AB||DC and its diagonals intersect each other at O show that AO/BO=CO/DO

Answer 1

AO / OC = OD /OC = BY REPLACING AO/OB= OD /OC

Answer 2

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Given, ABCD is a trapezium where AB || DC and diagonals AC and BD intersect each other at O.

Ncert solutions class 10 chapter 6-12

We have to prove, AO/BO = CO/DO

From the point O, draw a line EO touching AD at E, in such a way that,

EO || DC || AB

In ΔADC, we have OE || DC

Therefore, By using Basic Proportionality Theorem

AE/ED = AO/CO ……………..(i)

Now, In ΔABD, OE || AB

Therefore, By using Basic Proportionality Theorem

DE/EA = DO/BO…………….(ii)

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

AO/CO = BO/DO

⇒AO/BO = CO/DO

Hence, proved.