Circles

 

Resource Overview  Skill or Concept: 

Draw circles; identify and determine the  relationships between the radius, diameter,  chord, center, and circumference. (QT‐G‐237)   

 

Excerpted from: 

 

Key Curriculum Press  1150 65th Street, Emeryville, CA 94608  www.keypress.com  © Key Curriculum Press    

 

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KeyTo_Copyright_Geometry_SW2.pdf

8/6/10

3:56:29 PM

Key to

Geometry

2

® CIRCLES

Student Workbook

TABLE OF CONTENTS

To the Student

Drawing Circles

3

The Center of a Circle

7

The Radius of a Circle

11

Intersecting Circles

14

Comparing Segments

17

Circles with the Same Segment as Radius

24

Drawing a Segment Congruent to a Given Segment

26

These books will help you to discover for yourself many important relationships of geometry. Your tools will be the same as those used by the Greek mathematicians more than 2000 years ago. These tools are a compass and a straightedge. In addition, you will need a sharpened pencil. The lessons that follow will help you make drawings from which you may learn the most. The answer books show one way the pages may be completed correctly. It is possible that your work is correct even though it is different. If your answer differs, re-read the instructions to make sure you followed them step by step. If you did, you are probably correct.

Drawing a Circle with Radius Congruent to a Given Segment

29

Arcs

32

The Radius of an Arc

34

Comparing Segments

36

Equilateral Triangles

39

Intersecting Circles and Triangles

44

Constructing an Equilateral Triangle

47

Constructing Hexagons

50

Review

52

Practice Test

54

About the Cover In many societies the study of geometry began as the art of measuring and surveying land. Chinese geometry began this way. Ancient Chinese geometers searched for ways to easily subdivide fields into rectangular plots. They found that rectangular plots could be created by combining right triangles. The Chou Pei, the oldest known Chinese mathematics text, begins with a discussion of the properties of right triangles. The exact age of the Chou Pei is not certain but it is at least 2000 years old. On the cover of this booklet an ancient Chinese mathematician works on a page of the Chou Pei. The illustration represents a proof of an important theorem about right triangles. Although the theorem has been named after the Greek mathematician Pythagoras, Chinese geometers were familiar with the theorem and its proof centuries before the birth of Pythagoras.

Cover art by Howard Coale IMPORTANT NOTICE: This book is sold as a student workbook and is not to be used as a duplicating master. No part of this book may be reproduced in any form without the prior written permission of the publisher. Copyright infringement is a violation of Federal Law. Copyright © 1979, 1972 by Holden Day, Inc. All rights reserved. ® Key to Fractions, Key to Decimals, Key to Percents, Key to Algebra, Key to Geometry, Key to Measurement, and Key to Metric Measurement are registered trademarks of Key Curriculum Press. Published by Key Curriculum Press, 1150 65th Street, Emeryville, CA 94608 ISBN 978-0-913684-72-6 39 38 37 36 35 14 13 12 11 10