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Q: Which quadrilaterals must have diagonals of equal length?

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A square, a rhombus and a kite are all 4 sided quadrilaterals that have perpendicular diagonals.

Not for all trap. Only for an isosceles trapezoid. Well, for an Isosceles trapezoid, it could be any of the two diagonals! In order to have an isosceles trapezoid with the diagonals equal, the isosceles part MUST be precise and specific.

Nope, in order for the diagonals to be perpendicular the shape must be a square (which I guess is a type of rectangle :). The diagonals will cross, but not at a 90degree angle, unless the sides are of equal length.Not unless the rectangle has 4 equal sides, making it a squre.

A regular polygon has all its angles of equal measure, and its sides of equal length. In the case of a quadrilateral, that would mean a square. A concave quadrilateral must have at least one reflex angle and so cannot be a square. So it cannot be regular.

False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.

Related questions

Isosceles trapezoid and rectangle

A square, a rhombus and a kite are all 4 sided quadrilaterals that have perpendicular diagonals.

The diagonals of a parallelogram are congruent (equal in length) and bisect each other.

It is a square because its diagonals are equal in length and they bisect each other at right angles which is 90 degrees The diagonals of a rhombus are not equal in length but they meet at right angles.

A square has four equal length sides, a rectangle is a four sided shape with potentially different length sides --------------------- A rectangle can have sides of at most two different lengths and opposite sides must be equal. Also, both have four right angles, both have diagonals of equal length that bisect one another. Both (by virtue of being right angled) are cyclic quadrilaterals.

No, all quadrilaterals are trapeziums. I kite must have 2 pairs of adjacent sides equal in length.

There is only one regular quadrilateral, the square. A regular polygon must have equal sides and equal angles, and in the case of quadrilaterals that is a square.

Both are quadrilaterals with all sides of equal length. All four vertices of a square must be right angles whereas a rhombus has two pairs of equal angles.

The sides of a rhombus must all be the same length, but the angles do not need to be the same. The result is a diamond shape where the diagonals can be two different lengths.

Not for all trap. Only for an isosceles trapezoid. Well, for an Isosceles trapezoid, it could be any of the two diagonals! In order to have an isosceles trapezoid with the diagonals equal, the isosceles part MUST be precise and specific.

This is false for all rhomboids (a distinct parallelogram such that 4 sides are equal, and has non-right angles), since by congruency, a parallelogram can be flipped on its axis (with 2 closer vertices), producing 2 unequal length diagonals.

Nope, in order for the diagonals to be perpendicular the shape must be a square (which I guess is a type of rectangle :). The diagonals will cross, but not at a 90degree angle, unless the sides are of equal length.Not unless the rectangle has 4 equal sides, making it a squre.

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