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Warm UP Given: Circle O with mAB=35 Find mC O A C B
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Objective SWBAT prove the inscribed angle theorem in order to find angle measurements.
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Homework Finish classwork Complete p. 699 – 705 CR #6
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Exploration 1) Draw circle C. 2) Mark points D, T and K on the circle.
3) Draw chord DT. 4) Draw chord DK.
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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
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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
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Exploration 5) Measure TDK. 6) Draw radii CK and CT.
7) Measure TCK. What does this make the measure of arcTK?
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Exploration 8) Compare the arcTK’s measure to TDK.
What is their relationship?
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Inscribed Angle Thm An angle inscribed in an arc has a measure equal to one-half the measure of the intercepted arc.
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Inscribed Angle Theorem
K mTDK= ½ mTK
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Example Find the following: mURP mSP
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Exploration 9) Label point G somewhere on TDK.
10) Construct chords GT and GK. 11) Measure TGK How does this compare to mTDK?
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Congruent Inscribed Angles Theorem
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Example Find mLJM.
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Consider… If the arc is a semi-circle, what is the measure of the inscribed angle?
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Inscribed Angle Corollary
An angle inscribed in a semi-circle is a right angle. V D C O
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Example Find a, given WZY is a semi-circle.
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Classwork Practice – Inscribed Angles Show all work
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Summary We have had angles on the circle and at the center.
Where else could we place an angle?
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Homework Finish classwork Complete p. 699 – 705 CR #6
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