- Lesson 1: Points, Lines, and Angles
This lesson introduces the terminology and notation of basic geometric objects, with a focus on written and oral communication.
- Lesson 2: Triangles
We review how to classify triangles according to side lengths and angle measurements. We then investigate the side-angle relationship in triangles. This lesson concludes with an application of triangle properties to construct a 60-degree angle using a compass.
- Lesson 3: Angle Bisectors
A compass and a straightedge can be used to divide an angle in half perfectly without ever taking a measurement. In this lesson, we discuss the properties of angle bisectors and how to use these properties to construct an angle bisector of a given angle using only a compass and a straightedge. We extend our discussion to triangles and explore the relationship of the three angle bisectors in any triangle.
- Lesson 4: Perpendicular Bisectors
Continuing our discussion on constructions, we look at the properties of perpendicular bisectors and how to use these properties to construct a perpendicular bisector of a given line segment using only a compass and a straightedge. We extend our discussion to triangles and explore the relationship of the three perpendicular bisectors in any triangle.
- Lesson 5: Quadrilaterals
In this lesson, we look at the properties of six special quadrilaterals. We examine the similarities and differences between each and use a diagram to represent all of the relationships that we discuss.
- Lesson 6: Polygons
Expanding on quadrilaterals, in this lesson we discuss the properties of general polygons. In particular, we investigate the sum of the interior angles in a polygon and how polygons are connected to prisms. This lesson concludes with an extension that explores how prisms can be sliced to produce various polygonal faces.
- Lesson 7: Diagonals in Quadrilaterals
In this lesson, we investigate various properties of the diagonals in quadrilaterals. In particular, we consider when the diagonals bisect each other, are perpendicular to each other, or are equal in length. We then use these properties to help us classify quadrilaterals.
- Lesson 8: Circle Terminology
This lesson begins with a discussion of how to describe a circle. Since circles are very different from polygons, we introduce new terminology to use when studying circles. In particular, we define the centre, radius, diameter, and circumference of a circle. We also explore how to use polygons to help us estimate the circumference and the area enclosed by a circle.
- Lesson 9: Drawing Circles
In this lesson, we discuss strategies for drawing accurate circles. Specifically, we look at drawing circles when given a centre and a radius, a centre and a point that must lie on the circle, and also given two or more points that must all lie on the circle. We discuss where larger circles appear in the real world and what tools and strategies can be used to create them.
- Lesson 10: Applications of Circles
In this lesson, we take the application of circles beyond the wheel and discuss the role of circles in roundabout design, the use of circles in the design of structures, and how circles of different diameters interact in machines that use gears.