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.