Question

Question 1 :-) The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO=CO/DO∙ Show that ABCD is a trapezium.

Question 2:-) ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO=CO/DO∙

SOLVE MATHS EXPERT ​

Answer 1

$\huge\mathfrak\green{answer}$

1 :-)ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO=CO/DO∙

2:-) Given:

ABCD is a trapezium and AB∥DC

To Prove:

BOAA = DOCO

Construction:

Draw OE∥DC such that E lies on BC.

Proof:

In △BDC,

By Basic Proportionality Theorem,

OD

BO

= ECBBE

(1)

Now, In △ABC,

By Basic Proportionality Theorem,

OC

AO

= ECBE

(2)

∴ From (1), and (2),OCAO

= ODBO

i.e., BOAO = DOCO

Answer 2

Answer:

1 :-)ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that AO/BO=CO/DO∙

2:-) Given:

ABCD is a trapezium and AB∥DC

To Prove:

BOAA = DOCO

Construction:

Draw OE∥DC such that E lies on BC.

Proof:

In △BDC,

By Basic Proportionality Theorem,

OD

BO

= ECBBE

(1)

Now, In △ABC,

By Basic Proportionality Theorem,

OC

AO

= ECBE

(2)

∴ From (1), and (2),OCAO

= ODBO

i.e., BOAO = DOCO

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Step-by-step explanation:

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