Page 130 - IM_FL_Geometry_Print Sample

• What would happen if we move vertex that is on the circle? • Are there other angles it would be interesting to consider?
Activity Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about?” Encourage students to respectfully disagree, ask for clari cation or point out contradicting information. If the relationship between the two angle measures does not come up during the conversation, ask students to discuss this idea.
6.2 Right Triangles on a Segment
15 minutes
The purpose of this activity is to allow students to explore the relationship between right triangles and diameters of circles before looking at the more general case of inscribed angles. In a previous unit, students used coordinates to prove that triangles formed by connecting two endpoints of a diameter to a third point are right triangles. Here, they explore the converse of that statement, which is to observe that the set of right triangles whose hypotenuse is a given segment forms a circle with that segment as a diameter.
Launch
Tell students that they will use index cards to approximate right angles in this activity. Arrange students in groups of 2.
Student Task Statement
Here is segment . How can we describe all the right triangles that have segment as their hypotenuse? Here are some steps that will help you and your partner explore this question:
Unit 7 Lesson 6: The Angle Inscribed 57