College Geometry

[liawalters]

How do I prove the statement.................rectangles do not exist is true in hyperbolic geometry?............Please help and give some tips..............just finished 3 math courses and my brain is currently not functioning mathematical............haha

 

[pka]

How do I prove the statement.................rectangles do not exist is true in hyperbolic geometry?............Please help and give some tips..............just finished 3 math courses and my brain is currently not functioning mathematical............haha

Because we do not know exactly what your textbook/lecturenotes have to say about the definitions and axioms, it is very difficult to help you.

In most developments this is done using a Sacchri Quadrilateral.

 

[HallsofIvy]

Typically, one shows that the total measure of the three angles in a triangle is greater than 180 degrees. Then use the fact that a diagonal of a quadrilateral divides it into two triangles so that the total measure of angles in any quadrilateral is greater than 360 degrees. Of course, a "rectangle" is defined as a quadrilateral having four right angles which means its total angle measure must be exactly 360 degrees.