Lesson 4: 9-4 Inscribed Angles

1. How does a diagram help you make sense of a problem involving circles, angles, arcs, chords, etc.?
2. How does the relationship between an inscribed angle and its arc compared to that of a central angle and its arc?

Inscribed Angle
Intercepted Arc

G.C.2
Identify and describe relationships among inscribed angles, radii, and chords.
G.C.3
Construct inscribed and circumscribed circles of a triangle. Prove the properties of angles for a quadrilateral inscribed inside a circle.

An inscribed angle is an angle that has its vertex on the circle and its sides contained in chords of the circle. If an angle is inscribed in a circle, then the measure of the angle equals one-half of the measures of its intercepted arc. If two inscribed angles intercept congruent arcs or the same arc, then the angles are congruent.

The entrance to a school prom has a semicircular arch. Streamers are attached with one end at point A and the other end at point B. The middle of each streamer can then be attached to a different point P along the arch.

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 on a mix of problems including central angles, inscribed angles, chords, diameters, and radii.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.