Task

1 Task

Here is a trapezium ABCD. The point E is the intersection of the diagonals. Prove that the areas of triangles AED and BEC are equal.

2     parallel lines

Claim  1    AB || CD

Argument  1    By definition of trapezium, since ABCD is a trapezium.

3     same areas

Claim  1    area(△ABC) = area(△ABD)

Argument  1    Triangles △ABC and △ABD share the same basis AB and have equal heights because of #2.

4     areas of triangles

Claim  1    area(△ADE) = area(△BCE)

Argument  1    From the equal areas, see #3, of △ABC and △ABD we subtract the common area of △ABE. The remaining parts, △AED and △BCE, have the same area.