Geometry Syllabus

课程大纲 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.

目标学生 Who Should Take This Class?

  • 本课程适合8 - 9年级学生

  • This course is suitable for 8 - 9th grade students

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