Prove that the diagonals of a rectangle are congruent
Given a rectangle, prove that the diagonals are congruent.
: Rectangle ABCD
: 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.
AB ≅ segment DC
∠ABC ≅ ∠DCB
BC ≅ BC
Therefore, by SAS, triangle ABC ≅ triangle DCB.
Since triangle ABC ≅ triangle DCB, segment AC ≅ segment BD
Jan 18, 19 10:53 AM
This overtime calculator will help you figure out how much money earned for working overtime
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.