Degenerate Triangle

Date: 09/03/2003 at 19:37:32
From: Lisa
Subject: Degenerate Triangle

If a degenerate triangle is a triangle whose three vertices are 
collinear, is it not then just a straight line?

I'm having some difficulty picturing a "triangle" with three points in
a line.

Date: 09/03/2003 at 20:31:44
From: Doctor Rick
Subject: Re: Degenerate Triangle

Hi, Lisa.

Yes, the points of a degenerate triangle are the same as those of a 
single line segment. It consists of three points connected by line 
segments, but one of the points is on the "opposite" side, so the 
other two sides are parts of that first line segment.

Theorems derived from the definition of a triangle as three points 
connected by line segments will apply to this figure -- for instance, 
the sum of its angles is 180 degrees. However, it isn't what we 
picture when we say "triangle", and it isn't a very interesting 
triangle. That's why it's called degenerate. There are no points 
inside it; its area is zero. Some facts that are true of "ordinary" 
triangles are not true of a degenerate triangle: for instance, it 
does not lie in a unique plane. There are many planes in which all 
points of the degenerate triangle lie.

Does this help?

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 09/03/2003 at 21:18:10
From: Lisa
Subject: Thank you (Degenerate Triangle)

Thank you. I just wanted to make sure I had it straight.