Not necessarily........note this.....

Triangle ADC is the 180° rotation of the "supposed" right triangle ABC. Note that a parallelogram is formed - not a rectangle. The "hypotenuse" of each triangle - AC - is actually the diagonal of the parallelogram......!!!!
However, if ABC were a right angle....your supposition would be true.......a rectangle would be formed and the diagonal of this rectangle would be the two equal hypotenuses of both triangles.
