Learning Resources

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Outcomes

In this lesson you will learn

• develop definitions for and applications of arcs, central and inscribed angles, sectors
• discover relationships between arc and angle measures
• explore cyclic quadrilaterals and their properties

By the end of this section students will 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 withtangent 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

Mathematical Modeling, Book 3    p.232 - 251

In the context of the sports and activity centre, you will investigate arcs and sectors of circles and their relationship to the angles they subtend at the centre or on the circle. Inscribed angles, central angles and cyclic quadrilateral will be introduced and used in the problem. As well, the properties of tangents to a circle and their proofs are considered in light of the situation under study.

Applications using these ideas will be used throughout the section.

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:

• Euclidean proof
• vertical angles are congruent
• ability to measure angles with a protractor
• perpendicular lines