In this lesson, students encounter inscribed angles in circles, or angles formed by two chords that share an endpoint. Through experiment, students explore the relationship between inscribed angles and their associated central angles. They develop the conjecture that the measure of an inscribed angle is half the measure of the central angle that defines the same arc. Then, taking this conjecture as an assertion, they show that two intersecting chords and the segments joining adjacent endpoints of the chords create similar triangles. As students prove their conjectures and explain their reasoning, they have the opportunity to create arguments and critique the reasoning of others (MP3). As students refine their explanations, they increase their precision of language (MP6).

One of the activities in this lesson works best when students have access to devices that can run the applet because students benefit from seeing the relationship in a dynamic way.