# Geometry

## 1. Introduction to Geometry

1.1 Points, Lines, and Planes 1.2 Measuring Segments 1.3 Measuring Angles 1.4 Angle Pairs and Relationships 1.5 Midpoint and Distance Formulas 1.6 Perimeter and Area in the Coordinate Plane incomplete 1.7 Linear Measure 1.8 Two-Dimnensional Figures 1.9 Three-Dimensional Figures

## 2. Proofs and Reasoning

2.1 Inductive Reasoning 2.2 Conditional Statements 2.3 Biconditional Statements 2.4 Deductive Reasoning 2.5 Algebraic Reasoning and Proof 2.6 Geometric Reasoning and Proof 2.7 Proving Angle Relationships 2.8 Proving Segment Relationships 2.9 Logic 2.10 Postulates and Paragraph Proofs

## 3. Parallel and Perpendicular Lines

3.1 Lines and Angles 3.2 Properties of Parralel Lines 3.3 Proving Lines Parallel 3.4 Parralel and Perpedicular Lines 3.5 Constructions with Parallel and Perpendicular Lines 3.6 Equations of Lines 3.7 Slopes of Lines

## 4. Congruent Triangles

4.1 Congruent Figures 4.2 Triangle Conguence by SSS and SAS 4.3 Triangle Congruence by ASA and AAS 4.4 Isosceles and Equailateral Triangles 4.5 Classifying Triangles 4.6 Angles of Triangles 4.7 Triangles and Coordinate Proof

## 5. Relationships Within Triangles

5.1 The Triangle Midsegment Theorem 5.2 Perpendicular and Angle Bisectors 5.3 Bisectors of Triangles 5.4 Medians and Altitudes of Triangles 5.5 Indirect Proof 5.6 Inequalities in One Triangle 5.7 Inequalities in Two Triangles

6.1 Angles of Polygons 6.2 Properties of Parallelograms 6.3 Conditions for Parallelograms 6.4 Rectangles 6.5 Rhombi and Squares 6.6 Trapezoids and Kites 6.7 Proving That a Quadrilateral is a Parallelogram 6.8 Properties of Special Parallelograms

## 7. Similarity

7.1 Ratios and Proportions 7.2 Similar Polygons 7.3 Proving Triangle Similarity 7.4 Similarity in Right Triangles 7.5 Parallel Lines and Proportional Pairs 7.6 Parts of Similar Triangles 7.7 Scale Drawings and Models

## 8. Right Triangles and Trigonometry

8.1 The Pythagorean Theorem and Its Converse 8.2 Special Right Triangles 8.3 Trigonometry 8.4 Angles of Elevation and Depression 8.5 Law of Sines and Cosines 8.6 Solving Right Triangles 8.7 Vectors 8.8 Geometric Mean

## 9. Transformations

9.1 Translations 9.2 Reflections 9.3 Rotations 9.4 Congruence Transformations 9.5 Dilations 9.6 Similarity Transformations 9.7 Composition of Transformations 9.8 Symmetry

## 10. Area

10.1 Areas of Parallelograms and Triangles 10.2 Areas of Trapezoids, Rhombuses, and Kites 10.3 Areas of Regular Polygons 10.4 Permeters and Areas of Similar Figures 10.5 Areas of Circles and Sectors 10.6 Geometric Probability

## 11. Surface Area and Volume

11.1 Surface Areas of Prisms and Cylinders 11.2 Surface Areas of Pyramids and Cones 11.3 Volumes of Prisms and Cylinders 11.4 Columes of Pyramids and Cones 11.5 Surface Area and Volumes of Spheres 11.6 Congruent and Similar Solids 11.7 Representations of Three-Dimensional Figures 11.8 Spherical Geometry

## 12. Circles

12.1 Tangents 12.2 Arcs and Chords 12.3 Inscribed Angles 12.4 Angle Measures and Segment Lengths 12.5 Circles in the Coordinate Plane 12.6 Circles and Circumference 12.7 Measuring Angles and Arcs 12.8 Special Segments in a Circle 12.9 Equations of Circles 12.10 Angle Relationships in Circles 12.11 Segment Relationships

## 13. Probability

13.1 Permutations and Combinations 13.2 Conditional Probability Formulas 13.3 Representing Sample Spaces 13.4 Simulations 13.5 Probabilities of Independent and Dependent Events 13.6 Probabilities of Mutally Exclusive Events