Diagonal AC and Diagonal BD intersect each other in point O. complete the following and show AO/BO= CO/DO
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Answer:
Given:
ABCD is a trapezium and AB∥DC
To Prove:
BO
AO
=
DO
CO
Construction:
Draw OE∥DC such that E lies on BC.
Proof:
In △BDC,
By Basic Proportionality Theorem,
OD
BO
=
EC
BE
..(1)
Now, In △ABC,
By Basic Proportionality Theorem,
OC
AO
=
EC
BE
..(2)
∴ From (1), and (2),
OC
AO
=
OD
BO
i.e.,
BO
AO
=
DO
CO
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