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Lesson 6: The Angle Inscribed
• Know that inscribed angles on a diameter are right angles
• Recognize the relationship between inscribed angles and their corresponding central angles
Lesson Narrative
In this lesson, students explore the relationship between inscribed angles and their associated central angles. An angle inscribed in a circle is an angle whose vertex lies on the circle. Students are also introduced to the word chord to describe line segments whose endpoints lie on a circle. Through experiment, students develop the conjecture that the measure of an inscribed angle is half the measure of the central angle that traces out the same arc. In an optional activity, students can take this a step further by proving a case of the conjecture.
Students make sense of angle relationships when they use experiments to form conjectures (MP1).
Required Materials Geometry toolkits
Protractors
Required Preparation
Prepare 1 copy per student of the Blank Reference Chart blackline master (single sided).
Student Learning Goals
• Let’s look at angles inscribed in a circle.
6.1 Notice and Wonder: Angles and Circles
Warm Up: 5 minutes
The purpose of this warm-up is to elicit the idea that central angles are di erent than inscribed angles, which will be useful when students investigate their relationship in a later activity. While students may notice and wonder many things about these images, it is important to note that the inscribed angle is smaller than the associated central angle.
By engaging with this explicit prompt to take a step back and become familiar with a context and the mathematics that might be involved, students are making sense of problems (MP1). Students will go on to explore the relationship between inscribed and central angles. It is not necessary to introduce the vocabulary for chord or inscribed angle until later in the lesson.
Instructional Routines
• Notice and wonder
Unit 7 Lesson 6: The Angle Inscribed 55