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Absolutely. Any two congruent right triangles will form a rectangle, and if the right triangles are isosceles right triangles, they will form a square.
Yes. They can form a kite.
Not necessarly. If the sum of two of the sides congruent to each other are greater than that of the sides opposite them, then no. If however the kite forms a rombus ot square, the diagnoles will form four congruent triangles with the base of both being the line of symmetry.
Not always. You could form a kite. That means that the two adjacent sides would be congruent, not the two opposite sides.
a square or rhombus