Mathematics has become an integral part of the society in which we live. Geometry is one important aspect of mathematics, which can help students to relate to the world. In geometry students are exposed to a variety of problem-solving techniques and are taught how to communicate their reasoning for the mathematical choices they make.

* Description

In geometry students will study logic and investigate, discover, and apply geometric relationships such as lines, angles, polygons, circles, and solids through various techniques. Geometry students will use inductive, deductive, and indirect reasoning and write paragraph, two-column, and flowchart proofs. Geometry will provide students multiple real-world connections and abilities necessary for college.

* Units and Learner Objectives:

1. In geometry students will explore many kinds of patterns. They will also use transformations and symmetry as a basic tool in determining geometry relationships.

2. Students will discover properties of triangles, quadrilaterals, and other polygons, as well as prisms, through investigations.

3. Students will learn about postulates, definitions, properties and how they relate to deductive and inductive reasoning.

4. Students will explore distances and midpoints, equations of lines and the properties of parallel and perpendicular lines.

5. Students will analyze triangle inequalities and generalize relationships formed between angles formed by parallel lines and a transversal. Students will learn how adding auxiliary lines into a diagram may be helpful with deductive reasoning.

6. Students will study special triangles along with parallelograms. Students will explore area formulas.

7. Students will analyze circles and spheres. Students will investigate the relationships between tangents, secants, and chords.

8. Students will study coordinate matrices for transformations including dilations and translations.

RationaleMathematics has become an integral part of the society in which we live. Geometry is one important aspect of mathematics, which can help students to relate to the world. In geometry students are exposed to a variety of problem-solving techniques and are taught how to communicate their reasoning for the mathematical choices they make.

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DescriptionIn geometry students will study logic and investigate, discover, and apply geometric relationships such as lines, angles, polygons, circles, and solids through various techniques. Geometry students will use inductive, deductive, and indirect reasoning and write paragraph, two-column, and flowchart proofs. Geometry will provide students multiple real-world connections and abilities necessary for college.

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Units and Learner Objectives:1. In geometry students will explore many kinds of patterns. They will also use transformations and symmetry as a basic tool in determining geometry relationships.

2. Students will discover properties of triangles, quadrilaterals, and other polygons, as well as prisms, through investigations.

3. Students will learn about postulates, definitions, properties and how they relate to deductive and inductive reasoning.

4. Students will explore distances and midpoints, equations of lines and the properties of parallel and perpendicular lines.

5. Students will analyze triangle inequalities and generalize relationships formed between angles formed by parallel lines and a transversal. Students will learn how adding auxiliary lines into a diagram may be helpful with deductive reasoning.

6. Students will study special triangles along with parallelograms. Students will explore area formulas.

7. Students will analyze circles and spheres. Students will investigate the relationships between tangents, secants, and chords.

8. Students will study coordinate matrices for transformations including dilations and translations.

- __Chapter 12: Transformations__
- __Lesson 1__: Reflections
- __Lesson 2__: Translations
- __Lesson 3__: Rotations
- __Lesson 4__: Compositions of Reflections
- __Lesson 5__: Symmetry
- __Lesson 6__: Tessellations
- __Lesson 7__: Dilations

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