Mark Bauer

The Study of Geometry

**Why This Class is Important**

Geometry is one of the oldest fields of mathematics (2300 years) and one with many practical applications. Geometry is central to physics and engineering, introduces the idea of formal proof that forms the basis for higher-level mathematics, and is a prerequisite for Algebra 2, Pre-Calculus, and college mathematics. Geometry is required for high school graduation. Students who do not pass Geometry this year will be required to retake it until they pass. This may require summer school or a delay in graduation.

**Course Content**

The overall goals of this class are to develop skills in writing clear mathematical explanations, practice the 8 Standards for Mathematical Practice, and to cover the Geometry content standards in the Common Core State Standards of Mathematics.

## Geometry Overview

### Congruence

- Experiment with transformations in the plane
- Understand congruence in terms of rigid motions
- Prove geometric theorems
- Make geometric constructions

### Similarity, Right Triangles, and Trigonometry

- Understand similarity in terms of similarity transformations
- Prove theorems involving similarity
- Define trigonometric ratios and solve problems involving right triangles
- Apply trigonometry to general triangles

### Circles

- Understand and apply theorems about circles
- Find arc lengths and areas of sectors of circles

### Expressing Geometric Properties with Equations

- Translate between the geometric description and the equation for a conic section
- Use coordinates to prove simple geometric theorems algebraically

### Geometric Measurement and Dimension

- Explain volume formulas and use them to solve problems
- Visualize relationships between two-dimensional and three-dimensional objects

### Modeling with Geometry

- Apply geometric concepts in modeling situations

### Mathematical Practices

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.