Write a proof to show that a rectangle has congruent diagonals. be sure to create and name the appropriate geometric figures. this figure does not need to be submitted. (10 points)

answer:

given a rectangle, prove that the diagonals are congruent.

given: rectangle abcd

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.

summary

ab ≅ segment dc

∠abc ≅ ∠dcb

bc ≅ bc

therefore, by sas, triangle abc ≅ triangle dcb.

since triangle abc ≅ triangle dcb, segment ac ≅ segment bd

3 is greater then both of those numbers