Question

ABCD is a trapezium in which AB || DC and its
diagonals intersect each other at the point O. Show
ΑΟ/CO=BO/DO​

Answer 1

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Given parameters :

ABCD is a trapezium where AB || DC and diagonals AC and BD intersect at O.

To prove:

AOBO=CODO

Construction:

Draw a line EF passing through O and also parallel to AB

Now, AB ll CD

By construction EF ll AB

∴ EF ll CD

Consider the ΔADC,

Where EO ll AB

According to basic proportionality theorem

AEED=AOOC ………………………………(1)

Now consider Δ ABD

where EO ll AB

According to basic proportionality theorem

AEED=BOOD ……………………………..(2)

From equation (1) and (2) we have

AOOC=BOOD

⇒ AOBO=OCOD

Hence the proof.

Answer 2

Step-by-step explanation:

In ∆AOB and ∆COD, we have

<AOB=<COD [V.O.A.]

<BAO=<DCO [A.I.A.]

and <ABO=<CDO

then, by AAA similarity triangle ∆AOB------∆COD

Hence, AO/BO=CO/DO[Corresponding sides of similar triangles are in the same ratio]

Hope it will help U... UR frnd