6.4 Use Inscribed Angles and Polygons

1. 6.4Use Inscribed Angles and Polygons 6.3-6.4 Quiz: Friday

2. Vocabulary • An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.

3. Vocabulary • The arc that lies in the interior of an inscribed angles and has endpoints on the angle is called the intercepted arc of the angle.

4. Vocabulary • Measure of an Inscribed Angle Theorem • the measure of an inscribed angle is one half the measure of its intercepted arc. A 100o B 50o C

5. Vocabulary • Theorem 6.10 • If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

6. Vocabulary • A polygon is an inscribed polygon if all of its vertices lie on a circle. The circle that contains the vertices is a circumscribed circle. • Remember: a polygon is a closed figure made up of 3 or more straight lines.

7. Vocabulary • Theorem 6.11 • If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.

8. 90O 90O Vocabulary • Theorem 6.12 • A quadrilateral (4-sided figure) can be inscribed in a circle if and only if its opposite angles are supplementary (add up to be 180o)

9. Example: • Find the indicated measure in circle P. a) angle S b) arc RQ

10. You Try:

11. Example: • Find the value of each variable.

12. You Try: • Find the values of a and b.

13. Classwork/Homework • P. 207 #1 – 18