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TABLE OF CONTENTS |
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CH 4
CH 8
CH 12 |
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| CH 1 |
ESSENTIALS OF GEOMETRY | |
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SAT |
TE |
| 1-1 |
Undefined Terms | |
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| 1-2 |
The Real Numbers and Their Properties | |
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ACY |
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| 1-3 |
Definitions, Lines, and Line Segments | |
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| 1-4 |
Midpoints and Bisectors | |
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| 1-5 |
Rays and Angles | |
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| 1-6 |
More Angle Definitions | |
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| 1-7 |
Triangles | |
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ACY |
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| CH 2 |
LOGIC | |
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SAT |
TE |
| 2-1 |
Sentences, Statements, and Truth Values |
G.G.24 |
ACY |
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| 2-2 |
Conjunctions |
G.G.25 |
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| 2-3 |
Disjunctions |
ACY |
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| 2-4 |
Conditionals |
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| 2-5 |
Inverses, Converses, and Contrapositives |
G.G.26 |
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| 2-6 |
Biconditionals |
G.G.25 |
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| 2-7 |
The Laws of Logic | |
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| 2-8 |
Drawing Conclusions | |
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| CH 3 |
PROVING STATEMENTS IN GEOMETRY | |
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SAT |
TE |
| 3-1 |
Inductive Reasoning | |
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| 3-2 |
Definitions as Biconditionals | |
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ACY |
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| 3-3 |
Deductive Reasoning | |
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| 3-4 |
Direct and Indirect Proofs |
G.G.27 |
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| 3-5 |
Postulates, Theorems, and Proof |
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| 3-6 |
The Substitution Postulate |
ACY |
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| 3-7 |
The Addition and Subtraction Postulates |
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| 3-8 |
The Multiplication and Division Postulates |
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CH 4 |
CONGRUENCE OF LINE SEGMENTS, ANGLES, AND
TRIANGLES | |
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SAT |
TE |
| 4-1 |
Postulates of Lines, Line Segments, and Angles |
G.G.27
G.G.28
G.G.29 |
ACY |
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| 4-2 |
Using Postulates and Definitions in Proofs |
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| 4-3 |
Proving Theorems About Angles |
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| 4-4 |
Congruent Polygons and Corresponding Parts |
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| 4-5 |
Proving Triangles Congruent Using Side, Angle, Side |
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| 4-6 |
Proving Triangles Congruent Using Angle, Side, Angle |
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| 4-7 |
Proving Triangles Congruent Using Side, Side, Side |
ACY |
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| CH 5 |
CONGRUENCE BASED ON TRIANGLES |
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SAT |
TE |
| 5-1 |
Line Segments Associated with Triangles |
G.G.21
G.G.27
G.G.28
G.G.29
G.G.31
G.G.42 |
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| 5-2 |
Using Congruent Triangles to Prove Line Segments
Congruent and Angles Congruent |
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| 5-3 |
Isosceles and Equilateral Triangles |
ACY |
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| 5-4 |
Using Two Pairs of Congruent Triangles |
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| 5-5 |
Proving Overlapping Triangles Congruent |
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| 5-6 |
Perpendicular Bisector of a Line Segment |
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| 5-7 |
Basic Constructions |
G.G.17
G.G.18
G.G.19
G.G.20 |
ACY |
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| CH 6 |
TRANSFORMATIONS AND THE COORDINATE PLANE | |
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SAT |
TE |
| 6-1 |
The Coordinates of a Point in a Plane | |
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| 6-2 |
Line Reflections |
G.G.54
G.G.55
G.G.56
G.G.61 |
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| 6-3 |
Line Reflections in the Coordinate Plane |
ACY |
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| 6-4 |
Point Reflections in the Coordinate Plane |
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| 6-5 |
Translations in the Coordinate Plane |
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| 6-6 |
Rotations in the Coordinate Plane |
ACY |
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| 6-7 |
Glide Reflections |
ACY |
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| 6-8 |
Dilations in the Coordinate Plane |
G.G.58
G.G.59
G.G.61 |
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| 6-9 |
Transformations as Functions | |
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| CH 7 |
GEOMETRIC INEQUALITIES |
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SAT |
TE |
| 7-1 |
Basic Inequality Postulates | |
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ACY |
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| 7-2 |
Inequality Postulates Involving Addition and
Subtraction | |
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| 7-3 |
Inequality Postulates Involving Multiplication and
Division | |
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| 7-4 |
An Inequality Involving the Lengths of the Sides of
a Triangle |
G.G.33 |
ACY |
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| 7-5 |
An Inequality Involving an Exterior Angle of a
Triangle |
G.G.32 |
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| 7-6 |
Inequalities Involving Sides and Angles of a
Triangle |
G.G.34 |
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CH 8 |
SLOPES AND EQUATIONS OF LINES | |
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SAT |
TE |
| 8-1 |
The Slope of a Line | |
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| 8-2 |
The Equation of a Line | |
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ACY |
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| 8-3 |
Midpoint of a Line Segment | |
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| 8-4 |
The Slopes of Perpendicular Lines | |
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| 8-5 |
Coordinate Proof | |
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ACY |
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| 8-6 |
Concurrence of the Altitudes of a Triangle |
G.G.21 |
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| CH 9 |
PARALLEL LINES | |
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SAT |
TE |
| 9-1 |
Proving Lines Parallel |
G.G.35 |
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| 9-2 |
Properties of Parallel Lines |
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| 9-3 |
Parallel Lines in the Coordinate Plane | |
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| 9-4 |
The Sum of the Measures of the Angles of a Triangle |
G.G.30
G.G.32 |
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| 9-5 |
Proving Triangles Congruent by Angle, Angle, Side | |
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| 9-6 |
The Converse of the Isosceles Triangle Theorem |
G.G.31 |
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| 9-7 |
Proving Right Triangles Congruent by Hypotenuse, Leg |
G.G.21 |
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| 9-8 |
Interior and Exterior Angles of Polygons |
G.G.36
G.G.37 |
ACY |
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| CH 10 |
QUADRILATERALS |
G.G.38
G.G.39
G.G.41 |
SAT |
TE |
| 10-1 |
The General Quadrilateral |
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| 10-2 |
The Parallelogram |
ACY |
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| 10-3 |
Proving That a Quadrilateral Is a Parallelogram |
ACY |
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| 10-4 |
The Rectangle |
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| 10-5 |
The Rhombus |
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| 10-6 |
The Square |
ACY |
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| 10-7 |
The Trapezoid |
G.G.40
G.G.41 |
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| 10-8 |
Areas of Polygons | |
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| CH 11 |
THE GEOMETRY OF THREE DIMENSIONS | |
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SAT |
TE |
| 11-1 |
Points, Lines, and Planes |
G.G.1
G.G.2
G.G.3
G.G.4
G.G.7
G.G.8
G.G.9 |
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| 11-2 |
Perpendicular Lines and Planes |
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| 11-3 |
Parallel Lines and Planes |
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| 11-4 |
Surface Area of a Prism |
G.G.10 |
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| 11-5 |
Volume of a Prism |
G.G.11
G.G.12 |
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| 11-6 |
Pyramids |
G.G.13 |
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| 11-7 |
Cylinders |
G.G.14 |
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| 11-8 |
Cones |
G.G.15 |
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| 11-9 |
Spheres |
G.G.16 |
ACY |
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CH 12 |
RATIO, PROPORTION, AND SIMILARITY | |
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SAT |
TE |
| 12-1 |
Ratio and Proportion | |
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| 12-2 |
Proportions Involving Line Segments | |
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| 12-3 |
Similar Polygons | |
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ACY |
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| 12-4 |
Proving Triangles Similar |
G.G.44
G.G.45
G.G.46 |
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| 12-5 |
Dilations | |
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| 12-6 |
Proportional Relations Among Segments Related to
Triangles | |
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| 12-7 |
Concurrence of the Medians of a Triangle |
G.G.21
G.G.43 |
ACY |
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| 12-8 |
Proportions in a Right Triangle |
G.G.47 |
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| 12-9 |
Pythagorean Theorem |
G.G.48 |
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| 12-10 |
The Distance Formula | |
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| CH 13 |
GEOMETRY OF THE CIRCLE | |
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SAT |
TE |
| 13-1 |
Arcs and Angles | |
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| 13-2 |
Arcs and Chords |
G.G.49 |
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| 13-3 |
Inscribed Angles and Their Measures |
G.G.51 |
ACY |
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| 13-4 |
Tangents and Secants |
G.G.50 |
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| 13-5 |
Angles Formed by Tangents, Chords, and Secants |
G.G.51 |
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| 13-6 |
Measures of Tangent Segments, Chords, and Secant
Segments |
G.G.53 |
ACY |
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| 13-7 |
Circles in the Coordinate Plane | |
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| 13-8 |
Tangents and Secants in the Coordinate Plane | |
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| CH 14 |
LOCUS AND CONSTRUCTION | |
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SAT |
TE |
| 14-1 |
Constructing Parallel Lines |
G.G.19 |
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| 14-2 |
The Meaning of Locus |
G.G.22
G.G.23 |
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| 14-3 |
Five Fundamental Loci |
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| 14-4 |
Points at a Fixed Distance in Coordinate Geometry |
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| 14-5 |
Equidistant Lines in Coordinate Geometry |
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| 14-6 |
Points Equidistant from a Point and a Line |
ACY |
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INDEX | |
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