SOLUTION: How can you prove the converse of the diagonals of a rhombus are perpendicular.

Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: How can you prove the converse of the diagonals of a rhombus are perpendicular.      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   


Question 122081: How can you prove the converse of the diagonals of a rhombus are perpendicular.
Answer by Edwin McCravy(6936) About Me  (Show Source):
You can put this solution on YOUR website!
How can you prove the converse of the diagonals of a rhombus are perpendicular.

The only converse that one could have would be this:

"If the diagonals of a parallelogram are perpendicular, the parallelogram is a rhombus." 

We would have to be given that it was a parallelogram.


Maybe you meant this instead:

The diagonals of a rhombus are perpendicular bisectors of each other.

Then the converse would be:

"If the diagonals of a quadrilateral are perpendicular bisectors of 
each other, the quadrilateral is a rhombus.

drawing%28400%2C375%2C-5%2C5%2C-5%2C5%2C%0D%0A%0D%0Aline%28-3%2C0%2C0%2C4%29%2Cline%280%2C4%2C3%2C0%29%2Cline%283%2C0%2C0%2C-4%29%2Cline%280%2C-4%2C-3%2C0%29%2C%0D%0A%0D%0Aline%28-3%2C0%2C3%2C0%29%2Cline%280%2C-4%2C0%2C4%29+%29  

Repost and tell us which one it is, or if it is smoething else.
Then we'll prove it.

Edwin