Learning Resources

Outcomes

In this lesson you will

• Explore the relationship between the length of a chord of a circle and its distance from the centre of the circle.
• Explore the idea of the converse of a statement as it applies to chords of a circle.

By the end of this section you should be able to:

• Apply inductive reasoning to make conjectures in geometric situations.
• Investigate, and make and prove conjectures associated with chord properties of circles.
• Write proofs using various axiomatic systems and assess the validity of deductive arguments.
• Demonstrate an understanding of the concept of converse.
• Apply properties of circles.
• Solve problems involving the equations and characteristics of circles and ellipses.

Introduction

In this section you will investigate, make conjectures about, and apply chord properties in the context of building a domed arena for a sports and activity complex.

In this section you will see that there are many valid ways to prove conclusions using geometry.

This section will form the groundwork for the sections that follow, as it reviews and introduces theory that will be applied throughout the unit.

This section should take from 4 to 5 hours to complete.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• Circle, semicircle, radius, centre, diameter, chord.
• Parallel and perpendicular lines.
• Midpoint.