Question

10. Write a coordinate proof for the following theorem below. Include the given and prove statements.

If a quadrilateral is a square, then its diagonals are congruent.

Square ABCD and its diagonals have been drawn for you.

Answer 1

Square ABCD with side length a
distance AC = sqrt( (0 - a)^2 + (a - 0)^2 )
= sqrt( (-a)^2 + a^2 )
= sqrt(2a^2)
= a*sqrt(2)
distance BD = sqrt( (a - 0)^2 + (a - 0)^2 )
= sqrt( a^2 + a^2 )
= sqrt(2a^2)
= a*sqrt(2)
Since d(AB) = a*sqrt(2) and d(BD) = a*sqrt(2), d(AB) = d(BD)

Answer 2

Oh my goodness. Thank you so, so, so much for answering this! I appreciate it a lot. Thanks again! :)

Answer 3

You are very welcome.