Yes, if the four shaded triangles in the figure are congruent right triangles, does the inner quadrilateral have to be a square
Why should it be a square
If the four shaded triangles in a figure are congruent right triangles, it means that each of these triangles has the same shape and size.
The hypotenuses of the congruent right triangles are congruent. These will form the sides of the square
Since all the sides of a square equal, we can easily say that a square will be formed