Question

Abcd is a trapezium in which ab parallel to dc and to a b is equal to 3 dc find the ratio of the areas of triangle aob and triangle cod

Answer 1

Answer:

Step-by-step explanation:Ac and bd are the diagonals which intersect at O.

In Triangle AOB and Triangle COD

Angle AOB = Angle COD(AB||CD..Alt. int. Angles)

Angle ABO=Angle CDO(alt. Int. Angles)

By AA similarity criterion AOB ~ COD

We know that the ratio of area of two similar triangle is equal to the ratio of the square of their corresponding sides.

Ar(AOB)/ar(COD)=AB^2/CD^2

=(3CD)^2/CD^2

=9CD^2/CD^2

=9/1

Ar(AOB):Ar(COD) = 9:1