Question

The diagonals of a quadrilateral ABCD intersect each other at the point o such that AO/BO=CO/DO
Show that ABCD is a trapezium.
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Answer 1

Step-by-step explanation:

Answer in attachment pls.

Answer 2

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Given, Quadrilateral ABCD where AC and BD intersects each other at O such that,

AO/BO = CO/DO.

Ncert solutions class 10 chapter 6-13

We have to prove here, ABCD is a trapezium

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

EO || DC || AB

In ΔDAB, EO || AB

Therefore, By using Basic Proportionality Theorem

DE/EA = DO/OB ………(i)

Also, given,

AO/BO = CO/DO

⇒ AO/CO = BO/DO

⇒ CO/AO = DO/BO

⇒DO/OB = CO/AO …………..(ii)

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

DE/EA = CO/AO

Therefore, By using converse of Basic Proportionality Theorem,

EO || DC also EO || AB

⇒ AB || DC.

Hence, quadrilateral ABCD is a trapezium with AB || CD.