# Geometry

## GENERAL STUDIES

### Geometry

### Course Description

The primary focus of the course is geometric investigation, hypothesis formation and proof. This standard first course in geometry covers the required concepts of Euclidean geometry including definitions, postulates, and theorems. Areas of study include angles, parallel lines, congruent and similar triangles, rectilinear figures, polygons, polyhedral, circles and arc, the Pythagorean Theorem, introductory trigonometry, and constructions. In addition to including application problems which serve to review concepts of Algebra, the process of proving theorems is introduced.

### Course Objectives

- Logic and reasoning – Using inductive and deductive reasoning, evaluation conjectures and counter examples using conditional statements
- Points, Lines, Planes, and Angles – Classifying angles; identifying, describing, and applying properties of points, lines, planes, and angles; and recognizing and applying properties of parallel and perpendicular lines and planes
- Congruence and Similarity – Applying properties of congruent figures, using proportional reasoning, and applying properties of similar figures
- Polygons and Circles – Classifying polygons and applying their properties, applying the special properties of right triangles, using right triangle trigonometry, and applying the properties of circles
- Perimeter, Area, and Volume – Determining the perimeter and area of polygons, the circumference and area of circles, and the surface area and volume of three-dimensional figures
- Coordinate, Transformational, and Three-Dimensional Geometry – Visualizing representations of two- and three-dimensional shapes, applying basic properties of line reflections, translations, rotations, dilations, and their compositions, and connecting algebra and geometry using the coordinate plane

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### Scope and Sequence

**Discovering Points, Lines, Planes, and Angles**

- The Coordinate Plane
- Points, Lines, and Planes
- Using Formulas
- Measuring Segments
- Midpoints and Segment Congruence
- Exploring Angles
- Angle Congruence

**Connecting Reasoning and Proof**

- Inductive Reasoning and Conjecturing
- If-Then Statements and Postulates
- Deductive Reasoning
- Using Proof in Algebra
- Verifying Segment and Angle Relationships

**Using Perpendicular and Parallel Lines**

- Parallel Lines and Transversals
- Angles and Parallel Lines
- Algebra: Slopes of Lines
- Proving Lines Parallel
- Parallels and Distance

**Identifying Congruent Triangles**

- Classifying Triangles
- Measuring Angles in Triangles
- Exploring Congruent Triangles
- Proving Triangles Congruent
- Analyzing Isosceles Triangles

**Applying Congruent Triangles**

- Special Segments in Triangles
- Right Triangles
- Indirect Proof and Inequalities
- Inequalities for Sides and Angles of a Triangle
- The Triangle Inequality
- Inequalities Involving Two Triangles

**Exploring Quadrilaterals**

- Parallelograms
- Rectangles
- Squares and Rhombi
- Trapezoids

**Connecting Proportion and Similarity**

- Algebra: Using Proportions
- Exploring Similar Polygons
- Identifying Similar Triangles
- Parallel Lines and Proportional Parts
- Parts of Similar Triangles
- Fractals and Self Similarity

**Applying Right Triangles and Trigonometry**

- Geometric Mean and the Pythagorean Theorem
- Special Right Triangles
- Trigonometry: Ratios in Right Triangles
- Angles of Elevation and Depression
- Law of Sines
- Law of Cosines

**Analyzing Circles**

- Exploring Circles
- Angles and Arcs
- Arcs and Chords
- Inscribed Angles
- Tangents
- Secants, Tangents, and Angle Measures
- Special Segments in a Circle
- Algebra: Equations of Circles

**Exploring Polygons and Area**

- Polygons
- Tessellations
- Area of Parallelograms
- Area of Triangles, Rhombi, and Trapezoids
- Area of Regular Polygons and Circles

**Investigating Surface Area and Volume**

- Exploring Three-Dimensional Figures
- Nets and Surface Areas
- Surface Area of Prisms and Cylinders
- Surface Area of Pyramids and Cones
- Volume of Prisms and Cylinders
- Volumes of Pyramids and Cones
- Surface Area and Volume of Spheres
- Congruent and Similar Solids

**Continuing Coordinate Geometry**

- Graphing Linear Equations
- Algebra: Writing Equations of Lines
- Algebra and Statistics: Scatter Plots and Slopes
- Coordinate Proof
- Vectors
- Coordinates in Space

**Investigating Loci and Coordinate Transformations**

- What is a Locus?
- Algebra: Locus and Systems of Linear Equations
- Mappings
- Reflections
- Translations
- Rotations
- Dilations