Warm UP Given: Circle O with mAB=35 Find mC O A C B

Objective SWBAT prove the inscribed angle theorem in order to find angle measurements.

Homework Finish classwork Complete p. 699 – 705 CR #6

Exploration 1) Draw circle C. 2) Mark points D, T and K on the circle. 3) Draw chord DT. 4) Draw chord DK.

Inscribed Angle In steps 1 through 4, you drew an inscribed angle. An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle

Intercepted Arc An intercepted arc consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them. TK is the intercepted arc of TDK T D K

Exploration 5) Measure TDK. 6) Draw radii CK and CT. 7) Measure TCK. What does this make the measure of arcTK?

Exploration 8) Compare the arcTK’s measure to TDK. What is their relationship?

Inscribed Angle Thm An angle inscribed in an arc has a measure equal to one-half the measure of the intercepted arc.

Inscribed Angle Theorem K mTDK= ½ mTK

Example Find the following: mURP mSP

Exploration 9) Label point G somewhere on TDK. 10) Construct chords GT and GK. 11) Measure TGK How does this compare to mTDK?

Congruent Inscribed Angles Theorem

Example Find mLJM.

Consider… If the arc is a semi-circle, what is the measure of the inscribed angle?

Inscribed Angle Corollary An angle inscribed in a semi-circle is a right angle. V D C O

Example Find a, given WZY is a semi-circle.

Classwork Practice – Inscribed Angles Show all work

Summary We have had angles on the circle and at the center. Where else could we place an angle?

Homework Finish classwork Complete p. 699 – 705 CR #6