Question

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2. Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O.
If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.


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Answer 1

Step-by-step explanation:

Diagonals of a trapezium ABCD with AB∣∣DC intersect each other at the point O. If AB=2CD, find the ratio of area of triangle AOB and COD.

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ANSWER

Given,

ABCD is a trapezium with AB∣∣CD .......(1)

And

AB=2CD ......(2)

In the triangles AOB and COD,

∠DOC=∠BOA [vertically opposite angles are equal]

∠CDO=∠ABO [alternate interior angles ]

∠DCO=∠BAO

Thus,

△AOB≈△COD

By the similarity rule, the ratio of the areas of the similar triangles is the ratio of the square of corresponding sides.

therefore

Area (△AOB):Area (△COD)=AB

2

:CD

2

Area (△AOB):Area (△COD)=(2CD)

2

:CD

2

Area (△AOB):Area (△COD)=4CD

2

:CD

2

Area (△AOB):Area (△COD)=4:1

Hence, this is the answer.

Answer 2

Answer:

hii

Step-by-step explanation:

iam riya form India Delhi