Vertical angels
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No. The diagonals are perpendicular, but they dont have to be congruent.
No. In fact they are almost NEVER congruent.
Yes.
Rectangles do not have congruent lines. A square can always be called a rectangle. But a rectangle can't always be a square.
An obtuse triangle does not always have three congruent sides. An obtuse triangle can be any form that always has three angles.