Practice Makes Perfect Geometry | Date: 21 April 2011, 01:56
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An old joke tells of a tourist, lost in New York City, who stops a passerby to ask,
“How do I get to Carnegie Hall?” The New Yorker’s answer comes back quickly:
“Practice, practice, practice!” The joke may be lame, but it contains a truth. No
musician performs on the stage of a renowned concert hall without years of daily
and diligent practice. No dancer steps out on stage without hours in the rehearsal
hall, and no athlete takes to the field or the court without investing time and sweat
drilling on the skills of his or her sport.
Math has a lot in common with music, dance, and sports. There are skills to
be learned and a sequence of activities you need to go through if you want to be
good at it. You don’t just read math, or just listen to math, or even just understand
math. You do math, and to learn to do it well, you have to practice. That’s why
homework exists, but most people need more practice than homework provides.
That’s where Practice Makes Perfect: Geometry comes in.
Many students of geometry are intimidated by the list of postulates and theorems
they are expected to learn, but there are a few important things you should
remember about acquiring that knowledge. First, it doesn’t all happen at once. No
learning ever does, but in geometry in particular, postulates and theorems are
introduced a few at a time, and they build on the ones that have come before. The
exercises in this book are designed to take you through each of those ideas, stepby-
step. The key to remembering all that information is not, as many people think,
rote memorization. A certain amount of memory work is necessary, but what solidifies
the ideas in your mind and your memory is using them, putting them to
work. The exercises in Practice Makes Perfect: Geometry let you put each idea into
practice by solving problems based on each principle.
You’ll find numerical problems and problems that require you to use skills
from algebra. You’ll also see questions that ask you to draw conclusions or to plan
a proof. As you work, take the time to draw a diagram (if one is not provided) and
mark up the diagram to indicate what you know or can easily conclude. Write out
your work clearly enough that you can read it back to find and correct errors. Use
the answers provided at the end of the book to check your work.
With patience and practice, you’ll find that you’ve not only learned all your
postulates and theorems but also come to understand why they are true and how
they fit together. More than any fact or group of facts, that ability to understand
the logical system is the most important thing you will take away from geometry.
It will serve you well in other math courses and in other disciplines. Be persistent.
You must keep working at it, bit by bit. Be patient. You will make mistakes, but
mistakes are one of the ways we learn, so welcome your mistakes. They’ll decrease
as you practice, because practice makes perfect.
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