Yes, they can.
To demonstrate this draw a square on a sheet of paper. Draw a line diagonally from one corner to the one opposite. Cut along this line and you will have two triangles. Take them apart; if you put them together again in the right way you will have a square. Put together in different ways you can make an isosceles triangle or an equilateral parallelogram.
If you do the same thing beginning with a rectangle, you will be able to reassemble the triangles to form a rectangle, isosceles triangle or a (non-equilateral) parallelogram.
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square and 2 triangles put together
If you have 2 EQUILATERAL triangles, and you stack them on their respective hypotenuses, the result: SQUARE. If you have 2 ISOSCELES triangles, and you stack them on their respective hypotenuses, the result: RECTANGLE. If you have 2 OBTUSE triangles, and you stack them on their respective hypotenuses, the result: PARALLELOGRAM.
A minimum of 2 triangles are needed, but you can also make a rectangle with 3 or more triangles.
square and rhombus i think
Parallelograms of any form, a square, a rectangle, and a rhombus are just special parallelograms so all will form 2 pairs of isosceles triangles when a diagonal is drawn.