Author:Zlatan Magajna (Sat May 7 10:28:50 2022)
Source: C:\ Users\ zlata\ zm\ Proj\ GeoOKweb\ Doc19\ OkExamples\ OKG_Easy\ Trapezium2.pro

# 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.

## Notes