Geometry Syllabus
This course is offered exclusively as a one-on-one class and is not available in a small-group format.
Syllabus
1 Tools of Geometry
1.1 Points, Lines, and Planes
1.2 Linear Measure and Precision
1.3 Distance and Midpoints
1.4 Angle Measure
1.5 Angle Relationships
1.6 Two.Dimensional Figures
1.7 Three.Dimensional Figures
2 Reasoning and Proof
2.1 Inductive Reasoning and Conjecture
2.2 Logic
2.3 Conditional Statements
2.4 Deductive Reasoning
2.5 Postulates and Paragraph Proofs
2.6 Algebraic Proof
2.7 Proving Segment Relationships
2.8 Proving Angle Relationships
3 Parallel and Perpendicular Lines
3.1 Parallel Lines and Transversals
3.2 Angles and Parallel Lines
3.3 Slopes of Lines
3.4 Equations of Lines
3.5 Proving Lines Parallel
3.6 Perpendiculars and Distance
4 Congruent Triangles
4.1 Classifying Triangles
4.2 Angles of Triangles
4.3 Congruent Triangles
4.4 Proving Congruence—SSS, SAS
4.5 Proving Congruence—ASA, AAS
4.6 Isosceles Triangles
4.7 Triangles and Coordinate Proof
5 Relationships in Triangles
5.1 Bisectors, Medians, and Altitudes
5.2 Inequalities and Triangles
5.3 Indirect Proof
5.4 The Triangle Inequality
5.5 Inequalities Involving Two Triangles
6 Quadrilaterals
6.1 Angles of Polygons
6.2 Parallelograms
6.3 Tests for Parallelograms
6.4 Rectangles
6.5 Rhombi and Squares
6.6 Trapezoids
6.7 Coordinate Proof and Quadrilaterals
7 Proportions and Similarity
7.1 Proportions
7.2 Similar Polygons
7.3 Similar Triangles
7.4 Parallel Lines and Proportional Parts
7.5 Parts of Similar Triangles
8 Right Triangles and Trigonometry
8.1 Geometric Mean
8.2 The Pythagorean Theorem and Its Converse
8.3 Special Right Triangles
8.4 Trigonometry
8.5 Angles of Elevation and Depression
8.6 The Law of Sines
8.7 The Law of Cosines
9 Transformations
9.1 Reflections
9.2 Translations
9.3 Rotations
9.4 Tessellations
9.5 Dilations
9.6 Reading Math: Scalars and Vectors
9.6 Vectors
10 Circles
10.1 Circles and Circumference
10.2 Measuring Angles and Arcs
10.3 Arcs and Chords
10.4 Inscribed Angles
10.5 Tangents
10.6 Secants, Tangents, and Angle Measures
10.7 Special Segments in a Circle
10.8 Equations of Circles
11 Areas of Polygons and Circles
11.1 Areas of Parallelograms
11.2 Areas of Triangles, Trapezoids, and Rhombi
11.3 Areas of Regular Polygons and Circles
11.4 Areas of Composite Figures
11.5 Geometric Probability and Areas of Sectors
12 Extending Surface Area
12.1 Representations of Three.Dimensional Figures
12.2 Surface Areas of Prisms
12.3 Surface Areas of Cylinders
12.4 Surface Areas of Pyramids
12.5 Surface Areas of Cones
12.6 Surface Areas of Spheres
13 Extending Volume
13.1 Volumes of Prisms and Cylinders
13.2 Volumes of Pyramids and Cones
13.3 Volumes of Spheres
13.4 Congruent and Similar Solids
13.5 Coordinates in Space
Introduction
This course includes a thorough investigation of the theorems and properties of Euclidean geometry, including: lines, angles, polygons, circles and 3-dimensional solids.
Students will develop an understanding of logic, reasoning and proof, and apply existing knowledge of algebra to geometric concepts.
Students will investigate the definitions of sine, cosine, and tangent for acute angles of right triangles using the Pythagorean Theorem.
Who Should Take This Class?
This class is suitable for students who have already completed Algebra 1.