1. 9-4 Inscribed Angles Objectives: To recognize and find measures of inscribed angles. To find properties of inscribed angles.

2. Vocabulary Inscribed Angle Intercepted Arc

3. Inscribed Angle An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.

4. Intercepted Arc In this circle we would say that angle FAB intercepts arc FDB. Arc FDB is called the intercepted arc.

5. Theorem 9-4 If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc.

6. Example 1

7. Theorem 9-5 If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent.

8. Theorem 9-6 If an inscribed angle of a circle intercepts a semicircle then the angle is a right angle.

9. Theorem 9-7 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary