Take any rectangle ABCD. Draw diagonal BD and take any point E on BD. Draw AE and CE.
Compare the areas of triangles ECD and EAD. Make a GSP Sketch or click here to open one. Conjecture? Prove it.
Compare the areas of triangles EBC and EBA. Conjecture? Prove it.
Draw Rectangle ABCD on a sheet of paper and create the diagonal BD by folding. How would you locate a point E by paper folding so that the area of triangle ECD is equal to the sum of the areas of triangle EBC and triangle EBA?
*Problems suggested by Professor Stephen D. Comer, Department of Mathematics and Computer Science, The Citadel.