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

QuestionAnswer 1

Diagonals of a rectangle are always congruent.

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.

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