Respuesta :
The length of the diagonal DF is given by:
[tex]d=\sqrt{(b-0)^2+(0-a)^2}=\sqrt{b^2+(-a)^2}=\sqrt{a^2+b^2}[/tex]
The length of the diagonal EG is given by:
[tex]d=\sqrt{(b-0)^2+(a-0)^2}=\sqrt{b^2+a^2}=\sqrt{a^2+b^2}[/tex]
The diagonals are congruent.
[tex]d=\sqrt{(b-0)^2+(0-a)^2}=\sqrt{b^2+(-a)^2}=\sqrt{a^2+b^2}[/tex]
The length of the diagonal EG is given by:
[tex]d=\sqrt{(b-0)^2+(a-0)^2}=\sqrt{b^2+a^2}=\sqrt{a^2+b^2}[/tex]
The diagonals are congruent.
The diagonals of a rectangle are congruent because the length of EG is equal to the length of DF.
What are congruent rectangles?
Two rectangles are said to be congruent if their corresponding sides and the diagonals are equal.
D (0, b)
E (a, b)
F(a, 0)
G (0, 0)
The length of the diagonal DF :
[tex]DF= \sqrt{(b-0)^2+(0-a)^2} = \sqrt{b^2+a^2} = \sqrt{a^2+b^2}[/tex]
The length of the diagonal EG:
[tex]EG= \sqrt{(b-0)^2+(a-0)^2} = \sqrt{b^2+a^2} = \sqrt{a^2+b^2}[/tex]
Since the length of EG is equal to the length of DF
Hence, the diagonals of a rectangle are congruent.
Learn more about of rectangles here:
https://brainly.com/question/15019502
#SPJ5
