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
No. A small pentagon will have smaller diagonals than a large pentagon! However, all the diagonals of a regular pentagon will be congruent.
All quadrilaterals (four sided shapes) have 2 diagonals.
It has 2 diagonals in common with all other 4 sided quadrilaterals
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.
A square and a rectangle have diagonals of the same lengths.
rectangle and parallelogram
rectangle and parallelogram
there is nothing listed
Most quadrilaterals will not have congruent diagonals: rectangles (incl squares) and isosceles trapezium are the exception.
A square
square, rectangle and an isosceles trapezoid.