Notes 12.3/12.4 (Angles)

1. Notes 12.3/12.4 (Angles) Learning Targets: I can find the measure of an inscribed angle. I can find the measure of an angle formed by a tangent and a chord. I can find measures of angles formed by chords, secants and tangents.

2. Vocabulary Tangent– a line, ray or segment that intersects the circle at one point Chord - a segment whose endpoints are on the circle Secant– a line, ray or segment that intersects the circle at two points

3. Inscribed Angle Inscribed Angle: An angle whose vertex lies on a circle and whose sides are chords of the circle (or one side tangent to the circle). Examples: 3 1 2 4 Yes! No! No! Yes!

4. Inscribed Angle Theorem The measure of an inscribed angle is equal to ½ the measure of the intercepted arc. Y Inscribed Angle 110 55 Z Intercepted Arc

13. Example: Interior Angle Theorem 91 A C x° y° B D 85

14. ° 1 y ° 2 y ° ° x 3 x ° y ° x Exterior Angles An angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle. Two secants 2 tangents A secant and a tangent

15. Exterior Angle Theorem The measure of the angle formed is equal to ½ the difference of the intercepted arcs.

16. Example: Exterior Angle Theorem