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Q: What are all quadrilaterals with congruent diagonals?

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No. An isosceles trapezium (isosceles triangle with its apex removed) would have congruent diagonals but it is not a parallelogram.

All quadrilaterals have 2 diagonals

All quadrilaterals (four sided shapes) have 2 diagonals.

A trapezoid with congruent diagonals is an isosceles trapezoid.

no, for example a rhombus

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square

Rectangles

Not generally.

No. An isosceles trapezium (isosceles triangle with its apex removed) would have congruent diagonals but it is not a parallelogram.

Most quadrilaterals do not.

rectangle and parallelogram

rectangle and parallelogram

there is nothing listed

A square and a rectangle have diagonals of the same lengths.

Most quadrilaterals will not have congruent diagonals: rectangles (incl squares) and isosceles trapezium are the exception.

A square

square, rectangle and an isosceles trapezoid.

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