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

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

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Answer 1 · 2015-11-18T18:11:48

Diagonals of a rectangle are always congruent.

Explanation:

Proof

In a rectangle $A B C D$ $ABCD$ sides $A B$ $AB$ and $C D$ $CD$ are congruent and parallel, sides $A D$ $AD$ and $B C$ $BC$ are congruent and parallel, all internal angles are $90^{o}$ $90^o$ .

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

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