Do the diagonals of a rectangle bisect the vertexes?

Answer 1

No.

Draw a rect. with dimensions of 1" by 2''. Note the angle formed by the diagonals.

Now lengthen the rect. to 1'" by 10". The angle formed by the base and the diag. has to be reduced in order for the diagonal to travel to the new corner (with the same rect. height).

This is not an actual proof. You can calculate the angle but I am not certain you can do it with geometry--need trig. With trig., knowing the two sides (you know the hypotenuse with geometry too so you could use any of the trig functions), you can calculate the tangent of the angle in the 1"x2" rect, it is 0.5000. The length of the base increases by 8" for the second rect., which changes the value of the tangent (0.10000) which in turn changes the degree of the angle. The diag. of a square bisects the vertex but no so with rectangles.