Question

19
The diagonals of a quadrilateral ABCD intersect each other at the
AO BO
point O such that
Show that ABCD is a trapezium.
OC OD
[CBSE 2005, '08]​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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Answer:

Given: Quadrilateral ABCD in which diagonals AC and BD intersects each other at O such that AO/BO = CO/DO. Construction: Through O, draw line EO, where EO || AB, which meets AD at E. ⇒ AB || DC. Hence, quadrilateral ABCD is a trapezium with AB || CD

Step-by-step explanation:

Given:

The diagonals of a quadrilateral ABCD intersect each other at the point O such that BOAO=DOCO

i.e., COAO=DOBO

To Prove: ABCD is a trapezium

Construction:

Draw OE∥DC such that E lies on BC.

Proof:

In △BDC,

By Basic Proportionality Theorem,

ODBO=ECBE............(1)

But, COAO=DOBO (Given) .........(2)

∴ From (1) and (2)