ANGLES TRIANGLES
CHAPTER 1: BASIC CONCEPTS AND ANGLES
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1. BASIC CONCEPTS
A. MATHEMATICAL REASONING
B. THE BASIS OF GEOMETRIC ARGUMENT
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2. ANGLES
A. DEFINITION
B. REGIONS OF AN ANGLE
C. MEASURE OF AN ANGLE
D. CONGRUENT ANGLES
E. ANGLE BISECTOR
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3. TYPES OF ANGLE
A. TYPES OF ANGLE ACCORDING TO MEASURE
B. PAIRS OF ANGLES
C. PARALLEL LINES
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CHAPTER 2: TRIANGLES AND CONGRUENCE
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1. BASIC CONCEPTS
A. THE TRIANGLE AND ITS ELEMENTS
B. TYPES OF TRIANGLE
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2. PROPERTIES OF A TRIANGLE
A. RELATIONS BETWEEN ANGLES
B. RELATIONS BETWEEN ANGLES AND SIDES
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3. CONGRUENCE
A. THE CONCEPT OF CONGRUENCE
B. WORKING WITH CONGRUENT TRIANGLES
C. ISOSCELES, EQUILATERAL AND RIGHT TRIANGLES
D. THE TRIANGLE ANGLE BISECTOR THEOREM
–Computational Geometry
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CHAPTER 3: SIMILAR TRIANGLES
1. THE CONCEPT OF SIMILARITY
A. INTRODUCTION TO SIMILARITY
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2. THE ANGLE-ANGLE SIMILARITY POSTULATE
A. THE ANGLE-ANGLE (AA) SIMILARITY POSTULATE
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3. WORKING WITH SIMILAR TRIANGLES
A. THE SIDE-ANGLE-SIDE (SAS) SIMILARITY THEOREM
B. THE SIDE-SIDE-SIDE SIMILARITY THEOREM
C. THE TRIANGLE PROPORTIONALITY THEOREM AND THALES’ THEOREM
D. FURTHER APPLICATIONS
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4. FURTHER STUDIES
A. EUCLIDEAN RELATIONS
B. MEDIAN RELATIONS
–Transformational Geometry