Question

in a trapezium ABCD,diagonals AC and BD intersect at O .if AB=3CD,then find ratio of areas of triangles COD And AOB.

Answer 1

Step-by-step explanation:

Given In a trapezium ABCD, diagonals AC and BD intersect at O .if AB=3 CD, then find ratio of areas of triangles COD And AOB.

• Given AB = 3 CD
• Here AB is parallel to DC
• Now in triangle AOB and triangle DOC
• Angle AOB = angle DOC (vertically opposite angles)
• Also alternate angles are equal.
• Therefore triangle AOB is congruent to triangle DOC (by AA )
• Therefore ar(AOB) / ar(COD) = AB^2 / CD^2
•                                             = (3 CD)^2 / CD^2
•                                               = 9/1

             So ar (AOB) / ar (COD) = 9:1

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