Lesson 2: 9-2 Measuring Angles and Arcs

1. What is the relationship between a central angle and its corresponding arc measure?
2. How do you find the arc length from the central angle?

Central Angle
Arc
Minor Arc
Major Arc
Semicircle
Congruent Arcs
Adjacent Arcs
Arc Length
Radian Measure

G.C.2
Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G.C.5
Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality.

A central angle of a circle has the center of the circle as its vertex, and its sides are two radii of the circle. A central angle separates the circle into two arcs. A minor arc degree measure equals the measure of the central angle. The ratio of the arc degree measure to 360 is equal to the ratio of the arc length to the circumference.

The 13 stars of the Betsy Ross flag are arranged equidistant from each other and from a fixed point. The distance between consecutive stars varies depending on the size of the flag, but the measure of the central angle formed by the center of the circle and two consecutive stars is always the same.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections by working together with portions of multiple circles and seeing which pieces go together to create three different circles. They can compare their work with other groups.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.