Question

Show that a diagonal of a rectangle divides it into two congruent triangles

Answer 1

The two diagonals are congruent (same length). In the figure above, click 'show both diagonals', then drag the orange dot at any vertex of the rectangle and convince yourself this is so.

Each diagonal bisects the other. In other words, the point where the diagonals intersect (cross), divides each diagonal into two equal parts

Each diagonal divides the rectangle into two congruent right triangles. Because the triangles are congruent, they have the same area, and each triangle has half the area of the rectangle