which of the following have congruent diagonals?

square
rhombus
parallelogram
rectangle

i believe the answer is the square and rectangle.

I think so too.

what about a parallelogram?

Only rectangles (squares included) have congruent diagonals, because all their angles are congruent (90 degrees). If you have angles larger or smaller than 90 degrees it makes the diagonals different lengths.

oh yeah, that's right. Thank you very much!

You are correct! The square and rectangle both have congruent diagonals.

To understand why, let's first define what congruent diagonals mean. Congruent diagonals are diagonals that have the same length or measure.

A square is a quadrilateral with four equal sides and four right angles. Since all sides of a square are equal, the diagonals must also be equal in length. Therefore, a square has congruent diagonals.

Similarly, a rectangle is a quadrilateral with four right angles. However, unlike a square, a rectangle does not necessarily have equal sides. But what makes the diagonals of a rectangle congruent is that a rectangle has opposite sides that are equal in length. Since opposite sides are equal, the diagonals formed will also have the same length.

On the other hand, a rhombus and parallelogram do not have congruent diagonals in general. A rhombus is a quadrilateral with all sides equal but does not have right angles, which means that its diagonals will not be congruent in most cases. A parallelogram is a quadrilateral with opposite sides parallel and equal in length, but again, it does not have to have right angles, so the diagonals will not necessarily be congruent.

So, the square and rectangle are the only two options in the given list that have congruent diagonals.