1. Arcs and Angles Relationships between Arcs and Angles
These measures are still in Degrees

2. Inscribed Angle
The measure of an angle inscribed in a circle is one half the measure of the intercepted arc
Angle COR = arc CR
Angle CAR = ½ arc CR or ½ Angle COR

3. Inscribed Angles Intercepting the Same Arc
Inscribed angles that intercept the same arc are congruent
Angle PAQ and Angle PBQ both intercept arc PQ

4. Angles Inscribed in a Semicircle
If the two chords of the angle have endpoints of the diameter then the angle is 90 degrees One side of the triangle formed is the diameter

5. Cyclic Quadrilaterals
A quadrilateral inscribed in a circle All the vertices of the quad touch the circle The opposite angles of a cyclic quadrilateral are supplementary

6. Arcs By Parallel Lines
A line that intersects a circle at 2 points is called a secant Secant passes through a circle and contains a chord How is this different than a tangent? Parallel Lines intercept congruent arcs in a circle

7. Examples

8. Examples

9. Proving Conjectures
We did some of these in class Can you prove triangles congruent? Can you prove it is isosceles?

10. Examples

11. Example

12. Homework
Pg 327 1,2,3,4,5,11 and 13 Honors 16 and 17 Pg and 2