How do you divide a rectangle into 4 identical triangles?

Divide the rectangle in half, so you have two squares. Then cut each of these squares in half by drawing a straight line from the top left hand corner to the bottom right hand corner. Then you'll have four right angle triangles.

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A rectangle, divided in half need not give a square. Try it with an A4 sheet of paper.

A much simpler answer is to draw the two diagonals.