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

Answer 1

Diagonals of a rectangle are always congruent.

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.

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Answer 2

Sadie Adams

The diagonals of a rectangle are always congruent.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.