Question

10 The diagonals of a quadrilateral ABCD intersect each other at the point o such that
M
AO.CO
BO DO
BNShow that ABCD is a trapezium​

Answer 1

♧Answer♧

Given ABCD is a Quadrilateral where diagonal AC and BD intersect at O and AO/BO = CO/DO.

To Prove ABCD is a trapezium.

Construction Draw EF||AB passing through point O.

Proof

AO/BO = CO/DO (Given)

AO/CO = BO/DO ........(1)

Now,

In tri.ADB

EO||AB (By construction)

• AE/DE = BO/DO

= AE/DE = AO/CO (from equation 1)

Thus, tri.ADC

Line EO divides the triangle in same ratio.

• EO||DC

But we know that EO||AB

= EO||AB||DC

= AB||DC

One pair of opposite sides of Quadrilateral ABCD are parallel.

Hence, ABCD is a trapezium.

Proved

Answer 2

Step-by-step explanation:

क्रमचय एक निश्चित क्रम में बना बनाया है जिसको दी गई वस्तु में एक समय में कुछ या सभी को लेकर बनाया गया है

10 The diagonals of a quadrilateral ABCD intersect each other at the point o such that

M

AO.CO

BO DO

BNShow that ABCD is a trapezium