Learning Resources

Outcomes

In this lesson you will

• Prove other relationships about arcs and angles.
• Use the properties of arcs and angles developed to prove other relationships.
• Do calculations based on the properties of arcs developed so far.

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.

Prerequisites

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

• That vertically opposite angles are congruent.
• The properties of an isosceles triangle.
• How to write a Euclidean proof.
• The properties of chords and angles developed so far.
• How to calculate the area and circumference of a circle.