Constructing Angles in Standard Position

Date: 12/11/2003 at 17:23:50
From: Cody
Subject: Geometry-Constructing

I'm just learning to construct angles and I'm wondering if I should 
always make my beginning line to the right.  When I check the answer
key it is sometimes opposite of what I've constructed because I have
started my line pointing left instead of right.  Does this make a
difference?

Date: 12/12/2003 at 12:00:52
From: Doctor Peterson
Subject: Re: Geometry-Constructing

Hi, Cody.

As far as an assignment goes, if you are told to construct an angle 
with a certain measure, it doesn't make any difference which way it 
points. So your answers are right even if they don't look the same as 
the answer key (as long as the angle has the correct measure). Just
turn the key's picture to match your own if you need to. If your 120
degree angle was

            /
           /
          /
  -------+

and the book shows

  \
   \
    \
     +-------

they are the same angle. In fact, you could even have

      |
      |
      |
      +
        \
          \

like a clock, and there is nothing wrong with it.

On the other hand, it's not a bad idea to get used to starting with a 
ray pointing to the right; this is called "standard position", and is 
commonly assumed, especially when you do trigonometry. Your book 
tends to show angles that way out of habit, because that's the usual 
way we show angles.

But make sure you understand that an angle does not HAVE to be in 
standard position! That's the risk that textbook authors take when
they choose to show all their answers that way. Some students may miss
that point, and not realize that the three angles in this triangle are
all 60 degree angles, and are all congruent:

     +
    / \
   /   \
  +-----+

If you have any further questions, feel free to write back.

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