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### 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,

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Geometry
Elementary Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons

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