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### Geometry Class

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Date: 9/2/96 at 21:42:55
From: Kathy Miller
Subject: Geometry class

How can I survive my first year of high school geometry?  I am very
confused.  Even the first week's lectures about points and planes have
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```
Date: 9/3/96 at 18:27:24
From: Doctor Tom
Subject: Re: Geometry class

Hi Kathy,

Well, there's no guaranteed answer to your problem, but I can
make a few suggestions.

First off, geometry is often tough for people because it is pretty
different from any math you've ever done before - the emphasis is
usually not on numbers and measurement (although there is some), but
on thinking about simple geometric shapes (points, lines, triangles,
etc.).

The teacher may be trying to be more precise than you like at the
beginning.  For example, if you think of points as dots on a paper,
and lines as the pencil lines that connect them, you'll do fine.  Of
course, a "dot" should be really small, and a "mathematical dot" is
really, really, really tiny, so what you really need to imagine is a
perfect pencil, and so on.

Actually, geometry is a funny subject in that a lot of people who were
"good at" math before geometry have trouble in geometry class and
those who had trouble suddenly find themselves doing better.  The
reason is that geometry represents a different kind of thinking -
instead of thinking about symbols and calculations and stuff like
that, you need to think about shapes and be able to think about how
shapes interact.

For example, here's a question. Try to work it in your head, not with
a pencil.

Imagine drawing 2 triangles on a piece of paper.  What's the
maximum number of times you can get the lines to cross?

You'll find yourself thinking about sliding around triangles over each
other in your mind's eye, and you'll probably notice some sloppiness
in my question - what if the triangles lie exactly on top of each
other, or share edges, or whatever?  Eventually, you'll probably
decide that if they can't share edges, 6 crossings (arranged like a
Star of David) is about the best you can do.

But you didn't do this with calculations like in algebra class, did
you? Your "calculations" were more like moving shapes around in your
mind. Of course, you can use pencils too, and that's a great help,
and you MUST draw pictures of what the text says.

Get together with your friends and try to make sense of it. This can
work really well. Or find somebody who took the class last year to
work on it with you. Or maybe your parents can help.  Or you can ask
specific questions here, of 'Doctor Math'. Or look in other geometry
books - sometimes a different book will explain things in another way
that makes more sense to you.

I hope this helps a little.

-Doctor Tom,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry

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