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Logic
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Sentences, Statements and Truth Values (2.1)
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Conjunctions (2.2)
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Disjunctions (2.3)
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Conditionals (2.4)
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Inverses, Converses and Contrapositives (2.5)
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Biconditionals (2.6)
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Truth Tables, Tautologies and Logically Equivalent Statements (A1.4)
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The Laws of Logic (2.7)
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Law of Modus Tollens (A1.7)
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Invalid Arguments (A1.8)
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Chain Rule (A1.9)
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Drawing Conclusions (2.8)
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Logic Proofs (A1.13)
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| 2 |
Introduction and Definitions of Geometric Terms
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Undefined Terms (1.1)
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Points, Lines and Planes (11.1)
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Perpendicular Lines and Planes (11.2)
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Parallel Lines and Planes (11.3)
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The Real Numbers and their Properties (1.2)
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Definitions, Lines and Line Segments (1.3)
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Midpoints and Bisectors (1.4)
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Rays and Angles (1.5)
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More Angle Definitions (1.6)
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Triangles (1.7)
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The Sum of the Measures of the Angles of a Triangle ( 9.4)
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| 3 |
Introduction To Proof
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Inductive Reasoning (3.1)
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Definitions as Biconditionals (3.2)
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Deductive Reasoning (3.3)
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Direct and Indirect Proofs (3.4)
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Postulates, Theorems and Proof (5.5)
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The Substitution Postulate (3.6)
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The Addition and Subtraction Postulates (3.7)
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The Multiplication and Division Postulates (3.8)
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| 4 |
Parallel Lines
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he Slope of a Line (8.1)
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The Equation of a Line (8.2)
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Midpoint of a Line Segment (8.3)
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The Distance Formula (12.10)
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The Slope of Perpendicular Lines (8.4)
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Coordinate Proof (8.5)
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Proving Lines Parallel (9.1)
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Properties of Parallel Lines (9.2)
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Parallel Lines in the Coordinate Plane (9.3)
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| This topic 5 |
Triangles and Congruence
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The Sum of the Measures of the Angles of a Triangle ( 9.4)
- Isosceles and Equilateral Triangles (5.3)
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Congruent Polygons and Corresponding Parts (4.4)
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Proving Triangles Congruent Using SAS (4.5)
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Proving Triangles Congruent Using ASA (4.6)
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Proving Triangles Using SSS (4.7)
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Proving Triangle Congruent Using AAS ( 9.5)
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Proving Right Triangles Congruent by HL (9.7)
- The Converse of the Isosceles Triangle Theorem (9.6)
- Using Congruent Triangles to Prove Line Segments Congruent and Angles Congruent (5.2)
- Using Two Pairs of Congruent Triangles ( 5.4)
- Proving Overlapping Triangles Congruent (5.5)
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Line Segments Associated with Triangles (5.1)
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Perpendicular Bisector of a Line Segment (5.6)
- Concurrence of the Altitudes of a Triangle (8.6)
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| 6 |
Quadrilaterals
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Interior and Exterior Angles of Polygons (9.8)
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The General Quadrilateral (10.1)
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The Parallelogram (10.2)
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Proving that a Quadrilateral is a Parallelogram (10.3)
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The Rectangle (10.4)
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The Rhombus (10.5)
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The Square (10.6)
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The Trapezoid (10.7)
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Areas of Polgons (10.8)
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| 7 |
Inequalities
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Basic Inequality Postulates (7.1)
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Inequality Postulates Involving Addition and Subtraction (7.2)
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Inequality Postulate Involving Multiplication and Division (7.3)
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An Inequality Involving the Lengths of the Sides of a Triangle (7.4)
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An Inequality Involving an Exterior Angle of A Triangle (7.5)
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Inequalities Involving Sides and Angles of a Triangle (7.6)
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| 8 |
Similarity
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Ratio and Proportion (12.1)
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Proportions Involving Line Segments (12.2)
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Similar Polygons (12.3)
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Proving Similar Triangles (12.4)
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Proportional Reasoning Among Segments Related to Triangles (12.6)
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Concurrence of the Medians of a Triangle (12.7)
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Proportions in a Right Triangle (12.8)
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Pythagorean Theorem (12.9)
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| 9 |
Transformations
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The Coordinates of a point in a Plane (6.1)
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Line Reflections (6.2)
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Line Reflections in the Coordinate Plane (6.3)
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Point Reflections in the Coordinate plane (6.4)
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Translations in the Coordinate Plane (6.5)
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Rotations in the Coordinate Plane (6.6)
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Glide Reflections (6.7)
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Dilations in the Coordinate Plane (6.8)
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Dilations (12.5)
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Transformations as Functions (6.9)
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| 10 |
Circles
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Arcs and Angles (13.1)
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Arcs and Chords (13.2)
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Inscribed Angles and Their Measures (13.3)
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Tangents and Secants (13.4)
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Arcs Formed by Tangents, Chords and Secants (13.5)
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Measures of Tangent Segments, Chords and Secant Segments (13.6)
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Circles in the Coordinate Plane (13.7)
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Tangents and Secants in the Coordinate Plane (13.8)
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| 11 |
Measurements in 3-Dimensions
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| 12 |
Locus
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The Meaning of Locus (14.2)
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Five Fundamental Loci (14.3)
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Points at a Fixed Distance in Coordinate Geometry (14.4)
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Equidistant Lines in Coordinate Geometry (14.5)
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Points Equidistant From a Point and a Line (14.6)
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| 13 |
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