Learning Resources

Outcomes

In this lesson you will

• Be introduced to the terminology associated with arcs, including: minor arc, major arc, subtended angles, inscribed angle, central angle.
• Discover the relationship between the measure of an inscribed angle and a central angle intercepting the same arc.
• Discover the relationship between two inscribed angles intercepting the same arc.

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 angle relationships in circles.
• Write proofs using various axiomatic systems and assess the validity of deductive arguments.
• Investigate, and make and prove conjectures associated with tangent properties of circles.
• Apply properties of circles
• Solve problems involving the equations and characteristics of circles and ellipses.
• Develop and apply formulas for distance and midpoint.

Introduction

In this section you will investigate arcs and sectors of circles, and their relationship to angles they subtend at the centre or on the circle.

You will also determine the properties of inscribed angles, central angles, and cyclic quadrilaterals. As before, this will be done in the context of the sports and activity complex.

You will examine properties of tangents to a circle, and use various methods to prove these properties.

You will then use your knowledge of all these concepts and properties to solve practical problems.

This section should take between 6 and 8 hours to complete.

Prerequisites

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

• How to construct circles and chords and find the measure of angles with a protractor.
• The meaning of diameter, radius, semi-circle, and arc of a circle.
• That vertically opposite angles are congruent.
• The properties of an isosceles triangle.