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Lesson Synthesis
In this lesson, students proved that opposite angles in a cyclic quadrilateral are supplementary. Ask students,
• “What are some ways to tell a quadrilateral is not cyclic?” (If the perpendicular bisectors of the sides are not concurrent at a single point, then the quadrilateral is not cyclic. Also, if the quadrilateral has a pair of opposite angles that are not supplementary, then it is not cyclic.)
Ask students to add this theorem to their reference charts as you add it to the class reference chart:
The opposite angles of a cyclic quadrilateral are supplementary. (Theorem)
11.4 More Airports
Cool Down: 5 minutes
Student Task Statement
Before the towns of Washington, Franklin, and Spring eld could build their airport, the town of Greenville decided they wanted to join in. They hope to nd a location for the airport that is the exact same distance from all four town centers. Clare, however, claims that this goal is impossible. How does she know?
Unit 7
Lesson 11: Circles Outside of Quadrilaterals 115
