Question

ABCD is a trapezium in which AB parallel DC and it's diagonals interesct each other at the point Of show that AO/BO=CO/DO​

Answer 1

Step-by-step explanation:

ABCD is a trapezium in which AB parallel DC and its diagonals intersect each other at point O . show that AO/BO = CO/DO. ABCD is a trapezium where AB || DC and diagonals AC and BD intersect at O. Hence the proof.

Answer 2

Step-by-step explanation:

Given-

ABCD is a trapezium .

Diagonals AC and BD intersect each other at O.

To prove-

AO/BO=CO/DO

Construction-

Draw EF||BA||CD , meeting AD in E

Proof-

In ∆ABD , OE||AB

By basic proportionality theorem,

DO/OB=DE/AE. ------------- Equation 1

In ∆CDA , EO||BC

By basic proportionality theorem,

CO/OA=DE/AE. ------------- Equation 2

From equation 1 and 2 , we get

DO/OB=CO/OA

AO/BO=CO/DO

Hence, proved .......

Hope you have understood ...