Perpendicular lines intersect.
"lines" are infinitely long, if you want to say that anypoint on an infinitely long line bisects that line (which IS the case in several geometrical theories but not all!) then:
YES, perpendicular lines bisect each other.
otherwise:
NO, you cannot bisect something that is infinitly long.
They bisect each other at 90 degrees. They are the perpendicular bisectors of each other.
Yes. Because the diagonals are perpendicular to each other and intersect at their midpoints, they bisect each other.
With a compass and a straight edge and the lines must bisect each other at 90 degrees
Rectangle
Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.
They bisect each other at 90 degrees. They are the perpendicular bisectors of each other.
perpendicular and bisect each other
Yes. Because the diagonals are perpendicular to each other and intersect at their midpoints, they bisect each other.
Not necessarily - the diagonals of a rhombus bisect each other (they are perpendicular bisectors of each other), but are not equal.
With a compass and a straight edge and the lines must bisect each other at 90 degrees
Rectangle
square
Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.
Only for a square or rhombus (diamond shape). The diagonals of a rectangle bisect each other, but are not perpendicular and do not bisect the opposite angles they join.
Yes they bisect each other at 90 degrees
They are perpendicular and therefore bisect each other at right angles
If you are talking about the diagonals of a quadrilateral, the only quadrilateral that have diagonals that are perpendicular and bisect each other is a square, because a rectangle has bisecting diagonals, while a rhombus has perpendicular diagonals. And a square fits in both of these categories.