Are the diagonals equal in a rectangle

This is because a rectangle is a parallelogram with four right angles. If you consider the two triangles formed by two sides and a diagonal (e.g., $\triangle ABC$ and $\triangle DCB$ for a rectangle $ABCD$), they are congruent by the Side-Angle-Side (SAS) congruence criterion. Since $AB = DC$ (opposite sides of a rectangle), $BC = CB$ (common side), and $\angle ABC = \angle DCB = 90^\circ$, then the third sides, the diagonals $AC$ and $DB$, must be equal.