Can the diagonals of a trapezoid bisect each other?

EDIT : since there seems to be some issueabout the definition i will make it clearer. Any quadrangle with bissecting diagonals is a parallelogram no matter what! read more

Draw the diagonals of a trapezoid, for example, an isosceles trapezoid, thereby creating 4 triangles inside the trapezoid. Now assume the diagonals do bisect each other. The congruent corresponding sides of the top and bottom triangles with the included vertical angle would make the triangles congruent by the side-angle-side theorem. read more

EDIT : since there seems to be some issueabout the definition i will make it clearer. Any quadrangle with bissecting diagonals is a parallelogram no matter what! read more

The diagonals of an isosceles trapezoid have the same length and divide each other into segments of the same length. In the picture below, the diagonals AC and BD have the same length, that is AC = BD; and they divide each other in segments of the same length, that is, AE = DE and BE = CE. read more