# Reshaping plane geometry forms;congruent triangles

• Oct 21st 2008, 08:33 AM
Tim28
Reshaping plane geometry forms;congruent triangles
A rectangle could be reshaped into a parallelogram. Could a triangle be reshaped? I don't think so. What forms could be reshaped without tearing? Maybe this is algebraic topology; reshaping a doughnut into a coffee cup.

I mention congruent triangles because that is the context. I like to think that SSS, ASA, SAS uniquely determine a triangle.
• Oct 22nd 2008, 01:40 AM
HallsofIvy
Quote:

Originally Posted by Tim28
A rectangle could be reshaped into a parallelogram. Could a triangle be reshaped? I don't think so. What forms could be reshaped without tearing? Maybe this is algebraic topology; reshaping a doughnut into a coffee cup.

I mention congruent triangles because that is the context. I like to think that SSS, ASA, SAS uniquely determine a triangle.

What do you mean by "reshaping". From your reference to "topology" you might be allowing any continuous deformation- bending lines,etc.. In that case, any polygon can be reshaped to any other, or to a circle.

If you are referring only to changing the angles of a polygon, while leaving the sides of the same length, the the "SSS" congurence shows that you cannot "reshape" a triangle in that way- The lengths of the sides determines the angles.