SOLUTION: Is it possible without side lenghts, to prove that a rectangle missing one of its long sides is a square? The diagonals are drawn in. I think my professor may have left out some

Algebra ->  Rectangles -> SOLUTION: Is it possible without side lenghts, to prove that a rectangle missing one of its long sides is a square? The diagonals are drawn in. I think my professor may have left out some       Log On


   

Question 442490: Is it possible without side lenghts, to prove that a rectangle missing one of its long sides is a square? The diagonals are drawn in. I think my professor may have left out some critical information, but if she didn't I am totally stuck.
Thank you,
Gianni Maiorano
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Let s be the short side of your "rectangle." And let l be the long side. Let d be your diagonal.
Given the pythagorean theorem, your diagonal will be s%2Asqrt%282%29 if your rectangle is indeed a square.
Use s^2 + l^2 = d^2 to find l^2.
If d+=+s%2Asqrt%282%29 then s^2 +l^2 = 2s^2 and thus l^2 = s^2, hence l=s.
Since your long side and short side are actually the same length, then the rectangle is also a square.
Does this make sense?
------- EDIT
I see your teacher said without side lengths.
A rectangle can be broken into two triangles.
If the two sides are the same, then the two corresponding angles will be the same. Namely, they will both be 45º.
Check the angles formed by the triangle. If one of the angles is 45, then you're set. It would be a square.