Question

Are the diagonals of a rectangle always, sometimes or never congruent?

Answer 1

Diagonals of a rectangle are always congruent.

Explanation:

Proof

In a rectangle `ABCD` sides `AB` and `CD` are congruent and parallel, sides `AD` and `BC` are congruent and parallel, all internal angles are `90^o`.

Therefore, triangles `Delta ABC` and `Delta ABD` are congruent as right triangles with one cathetus `AB` shared among them and another pare of catheti, `BC` and `AD`, being congruent.

Hence, their hypotenuses `AC` and `BD` are congruent.