Q: Are the diagonals of a square always congruent?

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square

Square.

The diagonals are perpendicular, but not necessarily congruent.

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

Rhombus.

Related questions

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

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

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.

It is a square

the diagonals of a trepazoid always congruent?

square, rectangle and an isosceles trapezoid.

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

square

Only the square has.

square

Yes.

Yes.