IM Geo.7.2 Lesson: Inscribed Angles
What do you notice? What do you wonder?
Use the applet to answer the questions. Do not show the angle measures until you are told to.
Name the central angle in this figure.
Name the inscribed angle in this figure.
Move point around the circle. As you move this point, what happens to the measure of angle ? Show the angle measures to confirm.
Move points and to new positions. Record the measure of angles and . Repeat this several times.
Make a conjecture about the relationship between an inscribed angle and the central angle that defines the same arc.
Here is a special case of an inscribed angle where one of the chords that defines the inscribed angle goes through the center.
The central angle measures degrees, and the inscribed angle measures degrees. Prove that .
The image shows a circle with chords CD, CB, ED, and EB. The highlighted arc from point C to point E measures 100 degrees. The highlighted arc from point D to point B measures 140 degrees.
Prove that triangles and are similar.