Trapezoid.
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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 the diagonals of a kite bisect each other at 90 degrees.
A trapezoid Trapezoid - 2 congruent diagonals that do not bisect each other. No right angles and has 1 pair of opposite parallel sides.
A quadrilateral is a parallelogram if and only if its diagonals bisect each other (this should be in any geometry book)
No but the diagonals of a square bisect each other at right angles