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From Wikipedia: '...a kite, or deltoid, is a quadrilateral with two disjoint pairs of congruent adjacent sides, in contrast to a parallelogram, where the congruent sides are opposite.' In other words, a kite consists of two isosceles triangles joined at the base. Beginning with a particular isosceles triangle, it will always be possible to construct from it one kite that has equal diagonals (given that the kite may be either convex or concave). Hence an infinite number of kites do have equal diagonals, but many do not. A notable example of a kite that does have equal diagonals is a square.
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What is a quadrilateral with equal diagonals and no right angles?
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.
Are diagonals in a parallelogram equal in length?
the sides that are parallel of each other are equal. * * * * * True, but that was not the question! In general, the diagonals are not of equal length.
A quadrilateral with equal diagonals and no right angles?
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.
The diagonals of a square are equal in length?
Yes.
What quadrilateral has perpendicular diagonals that have 2 pairs of equal sides?
A kite fits this description.
