Question 988853: Give a coordinate proof that a parallelogram is a rectangle iff its diagonals are congruent.
I know how to prove the other way around but I'm kind of confused on how to prove this. So far, I plotted a rectangle with coordinates A(0,0), B(c,0), C(c,a), D(0,a). Since AC = BD,  . But where am I supposed to go from here and how does this prove that the parallelogram is a rectangle.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
What is a rectangle? It is a parallelogram with four right angles. If a parallelogram has one right angle, then it has four right angles. So if you can show that the measure of segment AB squared plus the measure of segment BC squared is equal to the measure of segment AC squared, then you have shown that triangle ABC is a right triangle where angle B is right. The rest is trivial.
Hint: Try the distance formula.
John
My calculator said it, I believe it, that settles it
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