Geometry Through Competitions

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Useful for school Geometry courses, Geometry competitions, Mathcounts Competitions, AMC 10/12 Competitions, and SAT II Subject Test.

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Table of Contents

Chapter 1. Angles 1

Chapter 2. Classification of Triangles 21

Chapter 3. Congruent Triangles 47

Chapter 4. Similar Triangles 71

Chapter 5. Pythagorean Theorem 94

Chapter 6. Geometric Inequality 114

Chapter 7. Trigonometry and Right Triangles 132

Chapter 8. Angle Bisector and Median 161

Chapter 9. Rectangles and Squares 187

Chapter 10. Parallelograms 216

Chapter 11. Trapezoid 240

Chapter 12. Polygons 265

Chapter 13. Perimeter And Areas 283

Chapter 14. Volume 304

Chapter 15. Circles - Angle 327

Chapter 16. Circles - Line Segment Calculation 341

Chapter 17. Area Method 364

Chapter 18. Geometric Probability 384

Index 398


ACKNOWLEDGEMENTS
The problems in this program are drawn from the following state wide math competitions (Geometry). We would like to thank them.

The North Carolina State High School Math Contest: The State Mathematics Contest was initiated in 1979. The contest is under the sponsorship of the North Carolina Council of Teachers of Mathematics and the State Department of Public Instruction (http://www.ncssm.edu/smc/).

Indiana State Math Contest: This annual contest is provided by the Indiana Council of Teachers of Mathematics (ICTM) and governed by policies approved by ICTM for Indiana Colleges and Universities to host Indiana students for the contest. This math contest has been approved by the Division of School Activities and the Indiana Association of School Principals (http://ictm.onefireplace.org/mathcontest).

Alabama Statewide High School Math Contest: This annual contest (32nd in 2013) is sponsored by Alabama Council Of Teachers Of Mathematics and The Alabama Association Of College Teachers Of Mathematics (http://mcis.jsu.edu/mathcontest/).

TMTA High School Math Contests: This contest (first math contest exam giving in 1957) is sponsored by the Tennessee Mathematics Teachers’ Association. The contest exams are prepared at least a year in advance by college or university math departments. They are administered on the same morning in April at numerous testing centers (usually colleges or universities) around Tennessee (http://www.tmta.info/contests.php).

ACTM State High School Mathematics Contest: This annual contest is conducted by The Arkansas Council of Teachers of Mathematics (ACTM) (http://www.actm.net/math-contest.html).

Illinois State High School Math Contest: This annual contest is conducted by The Illinois Council of Teachers of Mathematics (http://www.ictm.org/links/contest.html).

The UNC Charlotte High School Math Contest: (http://math2.uncc.edu/~hbreiter/problems/UNCC.html).