Letter Names for Triangles

Date: 05/16/2000 at 13:44:47
From: Bob Newman
Subject: Letter Names for Triangles

Hi, 

When a triangle is named by the letters of its vertices, why are the 
letters in the order they are? Could they be in any order? (For 
example: ABC, ACB, CBA, etc.) I'm comparing triangles and rectangles 
to their letter names on the answer sheet, and I don't see why they 
are named the way they are. Can you help me?

Thanks,
Bob Newman

Date: 05/16/2000 at 16:55:58
From: Doctor Rick
Subject: Re: Letter Names for Triangles

Hi, Bob.

Sometimes the order matters, but often it doesn't. It depends what the 
question is. 

One time when it matters is when you want to name the triangle that is 
congruent or similar to a particular named triangle. For instance, if 
triangle BAC is similar to triangle DEF, 

          A
          /\
         /   \                E
        /      \              /\
       /         \           /   \
      /____________\        /______\
     B              C      D       F

it means that angle B is congruent to angle D, angle A is congruent to 
angle E, and angle C is congruent to angle F. That's not the same as 
saying that triangle ABC is similar to triangle DEF. In that case, 
angle A is congruent to angle D, angle B is congruent to angle E, and 
angle C is congruent to angle F. The matching angles in the two 
triangles must be named in the same order.

When you name a rectangle (or any figure with more than 3 vertices), 
it's always important that you name the vertices in order either 
clockwise or counterclockwise around the figure. If I referred to this 
rectangle, ABCD,

     A ____B
      |    |
      |    |
      |    |
      |____|
     D     C

as rectangle ABDC, that would be wrong: it would describe this figure 
instead (which is not a rectangle):

     A____B
      \  /
       \/
       /\
      /__\
     D    C

You can't make this mistake with a triangle, because no matter in 
which order you put the vertices, they will go either clockwise or 
counterclockwise around the triangle. But I can imagine times when 
your teacher might want you to name the vertices in clockwise order, 
or else in counterclockwise order. You'd have to ask your teacher.

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