A followup to my previous question -
Assume we have rhombus
wxyz. If I draw a line from
y (opposite vertices), this would bisect angles
y and create two triangles,
wzy. If I show that the triangles overlap perfectly when reflected over
wy, does that imply
wxyz is a square? I believe it does because if angle
x are not 90, then they would not overlap. And if one angle of a rhombus is 90, then all are and it is a square.
NOTE: I am NOT asking about congruence. I realize that the triangles would be congruent. I am asking if they would perfectly overlap by only reflection if and only if the rhombus was a square.