Yes at right angles
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The diagonals of a square bisect each other at 90 degrees
Yes. Because the diagonals are perpendicular to each other and intersect at their midpoints, they bisect each other.
No, the diagonals of a trapezoid do not necessarily bisect each other. Only in an isosceles trapezoid, where the two non-parallel sides are congruent, will the diagonals bisect each other. In a general trapezoid, the diagonals do not bisect each other.
A circle!! * * * * * Wrong: the diagonals of a circle DO bisect each other. A triangle is a possible answer.
Square, rhombus and a kite have diagonals that bisect each other at 90 degrees