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Geometry/Notes 10.4

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Geometry/Notes 10.4

1. 1. SECTION 10.4Inscribed Angles
2. 2. INSCRIBED ANGLES How do I find the measure of an inscribed angle? How do I find the measures of the angles of an inscribed polygons?
3. 3. INSCRIBED ANGLE Inscribed Angle: Angle with the vertex on the circle and the sides are chords. Intercepted Arc: The arc created by the chords.
4. 4. INSCRIBED ANGLE Inscribed and central angles are different! Inscribed = Central =
5. 5. INTERCEPTED ARCS Which are the intercepted Arcs? Inscribed = Central =
6. 6. THEOREM 10.4 B D A C
7. 7. THEOREM 10.4 B D A C
8. 8. EXAMPLE
9. 9. THEOREM Theorem 10.6: If two inscribed angles of a circle intercept congruent arcs or the same arc, then the angles are congruent.A B A BD C D C
10. 10. THEOREM Theorem 10.7: If an inscribed angle intercepts a semicircle, the angle is a right angle.
11. 11. EXAMPLE
12. 12. THEOREM Theorem 10.8: If a quadrilateral is inscribed in a circle, then its opposite angle are supplementary.
13. 13. EXAMPLE
14. 14. HOMEWORK Page 549  #8, 10,  14 – 30 Even
15. 15. LESSON PLAN Intro  Add a new angle inside a circle, an inscribed angle. Then develop theorems about inscribed angles. Standards- 9. Supplies – slides, whiteboard, note sheets Timing: One day for notes, one day for a combined review of 10.3 and 10.4 and a quiz. Day 1:  Essential Questions- slides 2  Input-slides 3, 6, 9 – 11, 13  Guided Practice - slides 4, 5, 7, 8, 12, 14  Independent Practice – Book Work