Geometry Course Outline

This is my plan for Common Core Geometry so far. If you've taught this course in New York State, and have any insight, please comment!

CC Geometry Course Outline

1. First Day Business: Class Policies/Norms, Edmodo, Class Jobs, Getting to Know You
2. Set up INB: Pocket, TOC, Class Policies, Math Toolbox & Reference Sheet, Grade Record
3. What is Geometry? How is it different from Algebra and other math classes?
4. Undefined Terms: Point, Line, Plane & Definitions: Segment, Angle, Side, Collinear, Right/Acute/Obtuse Angles
5. Notation and Labeling Figures

Unit 1: Transformations

1. Transformations as Functions (+vocab: image, pre-image)
2. Symmetries
3. Rigid Transformations (Isometries) & Preserved Properties
4. Compositions of Transformations
5. Practice with Translations (with and without coordinates)
6. Practice with Reflections: reflect & find line of reflection
7. Reflections with Coordinates
8. Practice with Rotations: rotate & find center/angle of rotation
9. Rotations with Coordinates

Unit 2: Triangles

1. Segments in Triangles: medians, altitudes, angle bisectors, perpendicular bisectors
2. Linear Pairs, Vertical & Adjacent Angles
3. Complementary & Supplementary Angles
4. Sum of Interior Angles of a Triangle
5. Classifying Triangles by Side (Equilateral, Isosceles, Scalene) and by Angle (Acute, Right, Obtuse)
6. Exterior Angles of a Triangle
7. Isosceles Triangles
8. Triangle Inequalities
9. Pre-Proof Reasoning

Unit 3: Congruence

1. Congruent Figures
2. Rigid Motion and Congruence
3. Methods of Proving Triangles Congruent (SSS, SAS, ASA, AAS, HL)
4. Algebra Proofs (not in curric) as intro to Geometry Proofs
5. Proving Triangles Congruent (Mini Triangle Congruence Proofs)  ← Use Proof Blocks
6. Proving Triangles Congruent (Midpoints and Bisectors)
7. Proving Triangles Congruent (Linear Pair Supplementary Vertical Angles Medians Altitudes)
8. Proving Triangles Congruent (Substitution Transitive Addition Subtraction)
9. Angles and Parallel Lines: corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles
10. Algebraic Problems involving Angles and Parallel Lines + Proving Lines Parallel
11. Perpendicular Lines
12. Perpendicular Bisectors
13. Proving Triangles Congruent (Overlapping Triangles)
14. Corresponding Parts of Congruent Triangles (CPCTC)

Unit 4: Quadrilaterals

1. The Quadrilateral Family - properties of all quadrilaterals (4 sides, sum int angles 360)
2. Properties of Parallelograms
3. Parallelogram Proofs
4. Properties of Rectangles, Rhombuses, and Squares
5. Rectangle, Rhombus, and Square Proofs
6. Properties of Trapezoids and Kites
7. Midsegment of a Trapezoid
8. Mixed Practice Problems

Unit 5: Constructions & Concurrencies

1. Using a Compass and Straightedge: Copy a line segment, copy an angle
2. Bisect a Segment / Perpendicular Bisector, Bisect an Angle
3. Parallel through a Point
4. Perpendicular through a Point not/on a line
5. Construction: Regular Hexagon
6. Construction: Equilateral Triangle
7. Construction: Square
8. Construction: Reflections
9. Construction: Angles 90, 60, 45, 30
10. Construction: Altitude, Median, Angle Bisector in a Triangle
11. Construction: Congruent Triangles - SSS, SAS, ASA
12. Construction: Partition a Line Segment
13. Points of Concurrency
14. Centroid: Concurrent Medians
15. Orthocenter: Concurrent Altitudes
16. Circumcenter: Concurrent Perpendicular Bisectors
17. Incenter: Concurrent Angle Bisectors

Unit 6: Dilations & Similarity

1. Dilations
2. *Horizontal and Vertical Stretches
3. Dilations and Lines
4. Similarity
5. Midsegment of a Triangle
6. Side-splitter Theorem
7. Measurements in Similar Figures (perimeters, areas, volume)
8. Proving Similar Triangles
9. Radicals Review
10. Mean Proportional (Geometric Mean)
11. Mean Proportional in Right Triangles (HLLS & SAAS)
12. Pythagorean Theorem & Triples (Pythag Spiral for fun)
13. Special Right Triangle: 45-45-90
14. Special Right Triangle: 30-60-90
15. Trigonometric Ratios
16. Sine and Cosine of Complementary Angles
17. Trigonometry: Solving for a Side
18. Trigonometry: Solve for an Angle
19. Trigonometry: Word Problems (angle of elevation/depression)

Unit 7: Circles

1. Circle Basics
2. Circumference and Area (or save for unit 9??)
3. Arcs and Chords
4. Inscribed Angles
5. Radius and Tangents
6. Secants and Tangents
7. Angles, Chords, and Secants
8. Review Angle Rules
9. BIG Circles
10. Circle Proofs
11. Segment Rules: Secants and Tangents
12. Segment Rules: Intersecting Chords
13. Arc Length & Radian Measure
14. Area of Sectors
15. Inscribed and Circumscribed Polygons - angles, segments, constructions

Unit 8: Coordinate Geometry & Equations

1. Midpoint
2. Length/Distance
3. Slope
4. Partition a Directed Line Segment
5. Area and Perimeter on the Coordinate Plane
6. Coordinate Geometry Proofs: Triangles
7. Equations of Parallel Lines
8. Equations of Perpendicular Lines
9. Equations of Parabolas (?) as Conics
10. Review Completing the Square
11. Equations of Circles

Unit 9: Extending to 3 Dimensions

1. Types of Polygons (n-sides, regular)
2. Interior Angles of Polygons
3. Exterior Angles of Polygons
4. Area and Perimeter of Polygons
5. Area and Circumference of Circles
6. Right Prisms: Volume
7. Cavalieri’s Principle
8. Pyramids
9. Cylinders
10. Cones
11. Spheres and Hemispheres
12. Solids of Revolution
13. Modeling
14. Density