A square and a rectangle have diagonals of the same lengths.
rectangle and parallelogram
square, rectangle and an isosceles trapezoid.
Rectangles
rectangle and parallelogram
A square
rectangle and parallelogram
square, rectangle and an isosceles trapezoid.
square
Not generally.
Rectangles
Most quadrilaterals do not.
rectangle and parallelogram
there is nothing listed
Most quadrilaterals will not have congruent diagonals: rectangles (incl squares) and isosceles trapezium are the exception.
Parallelograms or isosceles trapezium.
A square
No. An isosceles trapezium (isosceles triangle with its apex removed) would have congruent diagonals but it is not a parallelogram.