# Geometry

## Course Summary

Build geometry fundamentals and increase your problem-solving ability by applying geometry concepts to calculate angles and intersecting lines, perimeters, polygons, area and volume, and more. Students develop their ability to justify conclusions by writing formal proofs for geometric theorems and begin the process of constructing these proofs independently. Students acquire the geometric fundamentals needed to succeed in more advanced math courses.

**Course Prerequisite(s):**Algebra 1

## Curriculum

This is a 2-semester course. We do not recommend taking both semesters simultaneously.

##### Unit 1: Geometry Beginnings

- Nets and Drawings for Visualizing Geometry
- Points, Lines and Planes
- Measuring Segments
- Measuring Angles
- Exploring Angle Pairs
- Midpoint and Distance in the Coordinate Plane

##### Unit 2: Geometric Reasoning

- Basic Constructions
- Patterns and Inductive Reasoning
- Conditional Statements
- Biconditionals and Definitions
- Deductive Reasoning
- Reasoning in Algebra and Geometry
- Proving Angles Congruent

##### Unit 3: Lines and Angles

- Lines and Angles
- Properties of Parallel Lines
- Proving Lines Parallel
- Parallel and Perpendicular Lines
- Parallel Lines and Triangles

##### Unit 4: Congruent Triangles

- Congruent Figures
- Triangle Congruence by SSS and SAS
- Triangle Congruence by ASA and AAS
- Using Corresponding Parts of Congruent Triangles
- Isosceles and Equilateral Triangles
- Congruence in Right Triangles
- Congruence in Overlapping Triangles

##### Unit 5: Relationships Within Triangles

- Mid-segments of Triangles
- Perpendicular and Angle Bisectors
- Bisectors in Triangles
- Medians and Altitudes
- Indirect Proof
- Inequalities in One Triangle
- Inequalities in Two Triangles

##### Unit 6: Right Triangles

- The Pythagorean Theorem and Its Converse
- Special Right Triangles
- Trigonometry
- Angles of Elevation and Depression
- Areas of Regular Polygons

##### Unit 7: Transformations

- Translations
- Reflections
- Rotations
- Compositions of Isometries
- Congruence Transformations

##### Unit 8: Similarity

- Similar Polygons
- Proving Triangles Similar
- Similarity in Right Triangles
- Proportions in Triangles
- Dilations
- Similarity Transformations

##### Unit 9: Polygons and Quadrilaterals

- The Polygon Angle-Sum Theorems
- Properties of Parallelograms
- Proving That a Quadrilateral is a Parallelogram
- Properties of Rhombuses, Rectangles and Squares
- Conditions for Rhombuses, Rectangles and Squares
- Trapezoids and Kites
- Applying Coordinate Geometry
- Proofs Using Coordinate Geometry

##### Unit 10: Perimeter and Area

- Perimeter and Area in the Coordinate Plane
- Areas of Parallelograms and Triangles
- Areas of Trapezoids, Rhombuses, and Kites
- Polygons in the Coordinate Plane

##### Unit 11: Surface Area and Volume

- Surface Areas of Prisms and Cylinders
- Surface Areas of Pyramids and Cones
- Volumes of Prisms and Cylinders
- Volumes of Pyramids and Cones
- Surface Areas and Volumes of Spheres
- Areas and Volumes of Similar Solids

##### Unit 12: Circles

- Circles and Arcs
- Areas of Circles and Sectors
- Tangent Lines
- Chords and Arcs
- Inscribed Angles
- Angle Measures and Segment Lengths

##### Unit 13: Probability

- Experimental and Theoretical Probability
- Permutations and Combinations
- Compound Probability
- Probability Models
- Conditional Probability Formulas