Question

the diaglonas of a rectangle
are congruent ​

Answer 1

Answer:

" The diagonals of a rectangle are congruent" means diagonals of a rectangle are same in length. All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other). All angles are right angles by definition.

Answer 2

that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB

Here is what is given: Rectangle ABCD

Here is what you need to prove: segment AC ≅ segment BD

Since ABCD is a rectangle, it is also a parallelogram.

Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.

BC ≅ BC by the Reflexive Property of Congruence.

Furthermore, ∠ABC and ∠DCB are right angles by the definition of rectangle.

∠ABC ≅ ∠DCB since all right angles are congruent.

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