Diagnostic pre-unit assessment
Diagnose students’ ability to • find the area of a circle and of a sector of a circle; • find measure of a sector angle when the sector partitions the circle into congruent pieces; • construct a perpendicular bisector; • find the distance between two given points on the coordinate plane.
Students begin this unit by working with circles on the coordinate plane and use the Pythagorean Theorem to derive the equation of a circle. They learn about radian measure and use similarity to derive the fact that the length of the arc intercepted by an angle is proportional to the radius of the circle. They develop a formula for the area of a sector of a circle and examine properties of central and inscribed angles in a circle along with their subtended arcs. Students also examine properties of tangent lines, radii, and intersecting chords and apply these properties to solve problems in a variety of contexts, including real-world situations.