1. Inscribed Angles
Geometry 11-3

2. Inscribed Angle Investigation
Using geometry tools, or a calculator
Draw a large circle
Create a central angle and an inscribed angle that share the same points on the circle
Compare the measures
Inscribed Angle Investigation

3. Inscribed Angle Theorem
The measure of an angle inscribed in a circle is half the measure of its intercepted arc
Inscribed Angle Theorem

4. Inscribed Angle Theorem

5. Inscribed Angle Investigation
Based on this last conjecture, what can do we know about an inscribed angle that intercepts a diameter of the circle?
Inscribed Angle Investigation

6. Angle Inscribed in a Semicircle Corollary
Angles inscribed in a semicircle are right angles
Angle Inscribed in a Semicircle Corollary

7. Inscribed Angle Investigation
Using geometry tools, or a calculator
Create a second inscribed angle with a different vertex, but with the same intercepted arc as before
What can you conclude about the measures of the two angles?
Inscribed Angle Investigation

8. Inscribed Angles Intercepting Arc Corollary
Inscribed angles that intercept the same arc are congruent
Inscribed Angles Intercepting Arc Corollary

9. Cyclic Quadrilateral Investigation
Cyclic Quadrilateral - A quadrilateral inscribed in a circle
Construct a large cyclic quadrilateral
Compare the measures of the angles
Cyclic Quadrilateral Investigation

10. Cyclic Quadrilateral Conjecture
The opposite angles in a cyclic quadrilateral are supplementary
Cyclic Quadrilateral Conjecture

11. Inscribed Angles

12. Thought Investigation
Imagine an inscribed angle, which we know is half the intercepted arc
Thought Investigation

13. Thought Investigation
One endpoint of the inscribed angle is on a tangent line
Thought Investigation

14. Thought Investigation
Move the vertex of the inscribed angle toward the tangent line, the angles value does not change, half the intercepted arc.
Thought Investigation

15. Thought Investigation
So what happens when the vertex reaches the tangent point?
Thought Investigation

16. Inscribed angles

17. Practice Problems

18. Practice Problems

19. Practice Problems

20. Practice Problems

21. Practice Problems

22. Practice Problems

23. Practice Problems

46. Pages 601 – 605
6 – 24 even, 33 – 35, 51 – 53
Homework