2. Warm – up 2.

3. Inscribed Angles Section 6.4

4. Standards MM2G3. Students will understand the properties of circles. b. Understand and use properties of central, inscribed, and related angles.

5. Essential Questions What are the important circle measurements?

6. Essential Questions How do I use inscribed angles to solve problems? How do I use properties of inscribed polygons?

7. Definitions Inscribed angle – an angle whose vertex is on a circle and whose sides contain chords of the circle Intercepted arc – the arc that lies in the interior of an inscribed angle and has endpoints on the angle inscribed angle intercepted arc

8. Measure of an Inscribed Angle Theorem If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.

9. Example 1 Find the measure of the blue arc or angle. a. b.

10. Congruent Inscribed Angles Theorem If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

11. Example 2

12. Definitions Inscribed polygon – a polygon whose vertices all lie on a circle. Circumscribed circle – A circle with an inscribed polygon. The polygon is an inscribed polygon and the circle is a circumscribed circle.

13. Inscribed Right Triangle Theorem If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.

14. Inscribed Quadrilateral Theorem A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.

15. Example 3 Find the value of each variable. a. b.

16. Practice Pages 207 2 – 18 even

17. Homework Page 209 2 – 26 even