## Geometry

Total Units: 15

This course requires students to think critically and use logic to prove mathematical theorems and principles. Topics covered in this course include logic and reasoning, distance and length, angles, polygons, circles, perimeter, area, the coordinate plane, transformations, trigonometry, volume, surface area, and probability. This course is best taken in between Algebra I and Algebra II. While not a direct successor to Algebra I, Geometry requires that students have a strong foundation of algebraic skills in order to manipulate equations and solve problems that arise in Geometry. By completing Geometry, students become better prepared for Algebra II, improving their problem-solving skills, abstract and critical thinking, spatial awareness, and logical reasoning.

### Pre-requisite Skills

- 1.1 Operations with Integers
- 1.2 Length Conversions in the Imperial System
- 1.3 Mass Conversion in the Imperial System
- 1.4 Capacity Conversions in the Imperial System
- 1.5 Length, Mass and Capacity Conversions in the Metric System
- 1.6 Estimation
- 1.7 Solving Multi-Step Equations and Using the Distributive Property
- 1.8 The Coordinate Plane

### Logic & Proofs

- 2.1 Introduction to Logic and Proofs
- 2.2 Conditions and Sets
- 2.3 Conditional Statements
- 2.4 Equivalence Properties
- 2.5 Writing Proofs

### Distance & Length

- 3.1 Introduction to Geometry
- 3.2 Segments, Rays and Length
- 3.3 Segment Addition Postulate
- 3.4 Overlapping Segments Theorem
- 3.5 Congruent Segments

### Angles, Lines & Transversals

- 4.1 Angles and Measure
- 4.2 Angle Additional Postulate
- 4.3 Congruent Angles
- 4.4 Angle Pairs
- 4.5 Lines, Planes, and Transversals
- 4.6 Transversals and Angle Pairs
- 4.7 Transversals and Parallel Lines
- 4.8 Perpendicular Lines

### Triangles

- 5.1 Introduction to Triangles
- 5.2 Classifying Triangles by Side Length
- 5.3 Classifying Triangles by Angles
- 5.4 Triangle Sum Theorem
- 5.5 The Exterior Angle Theorem
- 5.6 Ratio & Proportion
- 5.7 Similar Triangles
- 5.8 Using Similar Triangles to Solve Problems
- 5.9 Congruent Triangles
- 5.10 Congruent Triangles Part II
- 5.11 The Pythagorean Theorem

### Polygons

- 6.1 Introduction to Polygons
- 6.2 Classification of Polygons
- 6.3 Quadrilaterals - Rectangles
- 6.4 Quadrilaterals - Parallelograms
- 6.5 Quadrilaterals - Trapezoids
- 6.6 Interior & Exterior Angles of Polygons
- 6.7 Similar Polygons

### Circles

- 7.1 Introduction to Circles
- 7.2 Properties of Tangents Part I
- 7.3 Properties of Tangents Part II
- 7.4 Properties of Tangents Part III
- 7.5 Arcs and Central Angles
- 7.6 Arc Additional Postulate and Arc Length

### Perimeter

- 8.1 Introduction to Perimeter
- 8.2 Perimeter of Triangles
- 8.3 Perimeter of Quadrilaterals
- 8.4 Perimeter of Polygons
- 8.5 Circumference of a Circle
- 8.6 Perimeter of Irregular Shapes

### Area

- 9.1 Introduction to Area
- 9.2 Area of Squares and Rectangles
- 9.3 Area of Triangles
- 9.4 Area of Parallelograms
- 9.5 Area of Trapezoids
- 9.6 Area of a Circle
- 9.7 Area of a Sector
- 9.8 Area of Regular Polygons
- 9.9 Area of Irregular Shapes

### Geometry in the Coordinate Plane

- 10.1 Introduction to Geometry in the Coordinate Plane
- 10.2 Distance on a Coordinate Plane
- 10.3 Midpoint Formula
- 10.4 Length of Polygons in the Coordinate Plane
- 10.5 Perimeter in the Coordinate Plane
- 10.6 Area in the Coordinate Plane
- 10.7 Equation of a Circle
- 10.8 Calculating Slop Using Rise Over Run
- 10.9 Calculate Slope Using DyDx and Intercepts
- 10.10 Slope & Intercept Form of a Line
- 10.11 Parallel & Perpendicular Lines in the Coordinate Plane
- 10.12 Quadrilaterals in the Coordinate Plane

### Triangles

- 11.1 Triangles and Altitudes
- 11.2 Triangles and Medians
- 11.3 Triangles and the Perpendicular Bisectors
- 11.4 Triangles and Angle Bisectors
- 11.5 Solving Systems of Equations by Substitution
- 11.6 Solving Systems of Equations by Elimination
- 11.7 Triangles and the Orthocentre
- 11.8 Triangles and the Centroid
- 11.9 Triangles and the Circumcentre
- 11.10 Incentre

### Circles Pt. 2

- 12.1 Arcs and Chords Part I
- 12.2 Arcs and Chords Part II
- 12.3 Arcs and Chords Part III
- 12.4 Arcs and Chords Part IV
- 12.5 Inscribed Angles
- 12.6 Tangents, Secants, and Angles Part I
- 12.7 Tangents, Secants, and Angles Part II
- 12.8 Tangents, Secants, and Angles Part III

### Transformations

- 13.1 Introduction to Transformations
- 13.2 Translations
- 13.3 Reflections
- 13.4 Rotations
- 13.5 Dilations
- 13.6 Multiple Transformations & Applications

### 3D Geometry & Volume

- 14.1 Introduction to 3D Geometry
- 14.2 Volume of Rectangular Prisms
- 14.3 Volume of Other Prisms
- 14.4 Volume of Pyramids
- 14.5 Volume of Cylinders
- 14.6 Volume of Cones
- 14.7 Volume of Spheres

### 3D Geometry & Surface Area

- 15.1 Introduction to Surface Area
- 15.2 Surface Area of a Prism
- 15.3 Surface Area of Pyramids
- 15.4 Surface Area of Cylinders
- 15.5 Surface Area of Cones
- 15.6 Surface Area of Spheres