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In Fig. 4.170, A B C D is a trapeziu...

In Fig. 4.170, `A B C D` is a trapezium in which `A B∥ D C` and `A B=2\ D C` . Determine the ratio of the areas of ` A O B` and ` C O D` . (FIGURE)

Text Solution

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In `triangleAOB and triangleCOD`.
`angle1=angle2` ( vertically opposite angles)
`angle3=angle4` (alternate angles as AB||DC)
`triangleAOB~triangleCOD` (AA corollary)
`(ar(triangleAOB))/(ar(triangleCOD))=(AB^(2))/(CD^(2))`
( ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides)
`((2CD)^(2))/(CD^(2))` ( AB= 2CD, given)
`(4CD^(2))/(CD^(2))=4/1`
`ar(triangleAOB): ar(triangleCOD) 4:1`
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