the diagonal of a quadrilateral ABCD intersect each other at point O such that Ao/Bo=Co/Do.Show that ABCD ia a trapezium
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10th
Maths
Triangles
Basic Proportionality Theorem (Thales Theorem)
The diagonals of a quadrila...
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Asked on October 15, 2019 by
Shobana Gujral
The diagonals of a quadrilateral ABCD intersect each other at the point O such that
BO
AO
=
DO
CO
. Show that ABCD is a trapezium.
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ANSWER
Given:
The diagonals of a quadrilateral ABCD intersect each other at the point O such that
BO
AO
=
DO
CO
i.e.,
CO
AO
=
DO
BO
To Prove: ABCD is a trapezium
Construction:
Draw OE∥DC such that E lies on BC.
Proof:
In △BDC,
By Basic Proportionality Theorem,
OD
BO
=
EC
BE
............(1)
But,
CO
AO
=
DO
BO
(Given) .........(2)
∴ From (1) and (2)
CO
AO
=
EC
BE
Hence, By Converse of Basic Proportionality Theorem,
OE∥AB
Now Since, AB∥OE∥DC
∴ AB∥DC
Hence, ABCD is a trapezium.
Step-by-step explanation:
AO/BO=CO/DO
So ∆ AOB & ∆ COD are simillar.
so <OAB=<OCD.
there for AB||DC.
Hence ABCD is a trapezium.