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Take one of these trapezoids. Fold the acute angle onto the right angle as shown in the diagram.
Unfold the trapezoid and cut along the crease. You should have the square and one of the two smaller isosceles right triangles of the tangram.
Take the other one of these trapezoids. This time, fold the obtuse angle onto the opposite right angle as shown in the diagram.
Open and cut along the fold line. You should get the parallelogram and the second smaller triangle of the tangram.
You now have done your tangram puzzle formed out of seven pieces, called 'tans' :
All five triangles have the same shape but are of different sizes. We say that those triangles are similar.