1. Circles and inscribed angles
An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle

2. Intercepted arc
The arc formed by an inscribed angle is the intercepted arc of that angle. Arc AC is the intercepted arc of angle ABC

3. Theorem 47-1
The measure of an inscribed angle is equal to half the measure of its intercepted arc
m< ABC = 1/2 m arc AC
50o
25o

4. Theorem 47-2
If an inscribed angle intercepts a semicircle, then it is a right angle

5. Proving and applying inscribed angle theorem
1) name inscribed angle
2) name arc intercepted by it
3) if m< COD = 52,
find m <CBD D

6. Finding angle measures in inscribed triangles
Find the measures of the 3 angles in the triangle
90o

7. Theorem 47-3
If 2 inscribed angles intercept the same arc, then they are congruent

8. Theorem 47-4
If a quadrilateral is inscribed in a circle, then it has supplementary opposite angles.

9. Finding angle measures in inscribed quadrilaterals
<A = 4z ,
< C = 3z+5
Find <C