# OK Geometry Report : Task

Author:: | Zlatan Magajna -
Source: | C:\zm\Proj\GeoOkApp\OkExamples\Trapezium2.pro
Comment: |

## 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.

### WORKOUT

| 2 parallel lines - AB|CD - AB|CD | By definition of trapezium, since ABCD is a trapezium..
| 3 areas of triangles - ABC~ABD - ABC~ABD | Triangles ABC and ABD have the same basis and equal heights because of #2.
| 4 areas of triangles - ADE~BCE - ADE~BCE | From the equal areas, see #3, of ABC and ABD we subract the common area of ABE. The remaining parts, AED and BCE, have the same area.

## Notes