Question

Prove that the
that the diagonals of a
rectangle ore congruent​

Answer 1

to prove 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.

Summary

segment AB ≅ segment DC

∠ABC ≅ ∠DCB

BC ≅ BC

Therefore, by SAS, triangle ABC ≅ triangle DCB.

Since triangle ABC ≅ triangle DCB, segment AC ≅ segment BD

Answer 2

a ____________________b

l.

l. l

d l___________________l c

let the diagonals are db ànd ca.

so triangle adb and abc are formed

ab=ab common

ad=bc( opposite sides of rectangle are equal

/_dab=/_CBA=90°

so by SAS

triangle adb is congurent to triangle ABC

so diagonals db=ca

may this help you