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An isosceles trapezoid will have diagonals of equal length but will never contain right angles by definition. A square and rectangle will have diagonals of equal length but will contain 4 right angles. A rhombus and any other parallelogram that does not contain right angles will not have diagonals of equal length.

Q: A quadrilateral with equal diagonals and no right angles?

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A Rhombus * * * * * WRONG! A rhombus does not have equal diagonals. If it did it would be a square! The shape is a special case of a kite.

It's impossible for a quadrilateral to have no equal sides and have right angles.

square and rectangle * * * * * No. Square and Kite but NOT rectangle.

It is a parallelogramIf one of the angles is a right angle (then they all are) and the quadrilateral is a rectangle.If both pairs of sides are equal in length (but none of the angles is a right angle) the quadrilateral is a rhombus.If the sides are equal and one of the angles is a right angle, the quadrilateral is a square.

you can prove any one of these statements to prove that quadrilateral is a rectangle: -- Opposite sides are parallel and any one angle is a right angle. -- Opposite sides are equal and any one angle is a right angle. -- All four angles are right angles. -- Adjacent angles are complementary, and one of them is a right angle. -- Opposite sides are either equal or parallel, and area is equal to the product of two adjacent sides. -- Diagonals are equal.

Related questions

kite

It is an isosceles trapezoid.

A rhombus is a 4 equal sided quadrilateral with equal opposite acute angles and equal opposite obtuse angles with diagonals that bisect each other at right angles.

Rhombus rhombus

quite

Two pairs of equal sides and four right angles.

A Quadrilateral Kite!

If the diagonals of a quadrilateral are perpendicular to each other, then the quadrilateral is a square.Or a kite.

Rhombus and square are the only quadrilaterals whose diagonals bisect the angles of the quadrilateral. In both these quadrilaterals, the diagonals intersect at right angles, dividing each angle into two equal parts.

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 parallelogram is one of them.

A Rhombus * * * * * WRONG! A rhombus does not have equal diagonals. If it did it would be a square! The shape is a special case of a kite.