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Answer 1

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Asked on December 26, 2019 by

Sahith Dambal

Prove that the diagonals of a trapezium divide each other proportionally.

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ANSWER

Given :

A trapezium ABCD in which AB∥DC and its diagonals AC and BD intersect at O.

To prove :

OC

AO

=

OD

BO

Construction :

Through O, draw EO∥AB, meeting AD at E.

Proof :

In △ADC,EO∥DC

Therefore,

ED

AE

=

OC

AO

.........(1)

In △DAB,EO∥AB

Therefore,

ED

AE

=

OD

BO

..........(2)

From 1 and 2, we get,

OC

AO

=

OD

BO

Hence, proved.

solution

Step-by-step explanation:

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Answer 2

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