Unit Overview:
In this unit, students will prove theorems about circles and study relationships among segments on chords, secant lines and tangent lines, as well as angles in circles. Students will recall information about trigonometry with inscribed and circumscribed circles of a triangle. They will further define angles of a circle using radian measures and derive the formula for the area of a sector. They will use the areas of circles to find the surface areas of cylinders and cones.
Enduring Understanding:
Essential Questions:
In this unit, students will prove theorems about circles and study relationships among segments on chords, secant lines and tangent lines, as well as angles in circles. Students will recall information about trigonometry with inscribed and circumscribed circles of a triangle. They will further define angles of a circle using radian measures and derive the formula for the area of a sector. They will use the areas of circles to find the surface areas of cylinders and cones.
Enduring Understanding:
- Discover relationships between angles made with chords, secant segments and tangent segments and apply theorems involving them.
- Using the properties of similarity, you can solve for the length of the arc, the area of the segment, and the area of the sector of a circle using the circumference or the area of a circle.
Essential Questions:
- How many different kinds of angles can be made with radii, chords, secants and tangents? What is the relationship between those angles and the arcs they intercept?
- How can similar triangles (inscribed or circumscribed by a circle) be used to prove the relationships between radii, chords, secants, tangents and the arcs they intercept?
- How can you solve for the arc length, segment, and sector of a given circle?
