SOLUTION: In a trapezoid ABCD with legs AB and CD, the diagonals intersect each other at point O. Compare the areas of triangle ABO and triangle CDO

Question 1174326: In a trapezoid ABCD with legs AB and CD, the diagonals intersect each other at point O.
Compare the areas of triangle ABO and triangle CDO
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

They are equal.

Triangles BCA and BCD have the same area, because they have the same base AB, and because the height of both triangles is the distance between the bases AD and BC.

The area of triangle ABO is the difference between the areas of triangles ABC and BCO.
The area of triangle CDO is the difference between the areas of triangles BCD and BCO.

Therefore the areas of triangles ABO and CDO are equal.

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