Q: What shapes diagonals will not always be congruent?

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congruent right triangels

No. The diagonals of a parallelogram are congruent if and only if the parallelogram is a rectangle.

A regular polygon.

If you mean an isosceles triangle then no because all triangles have no diagonals

It is a square

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the diagonals of a trepazoid always congruent?

No. The diagonals are perpendicular, but they dont have to be congruent.

congruent right triangels

Yes the diagonals of a square are always congruent. Their length is a*root 2 where a is the side of the square.

No. The diagonals of a parallelogram are congruent if and only if the parallelogram is a rectangle.

In a quadrilateral, the diagonals are only congruent for rectangles (or squares, which is a special kind of rectangle). Note: they are not congruent for a Rhombus.

Regular polygons. A square and rectangle will have congruent (equal length) diagonals.

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

rectangle and parallelogram

A regular polygon.

The diagonals of a square. Each equals to s√2, where s is the side-length of the square. A rectangle and an isosceles trapezoid also have congruent diagonals.

If you mean an isosceles triangle then no because all triangles have no diagonals