1. Tab 1 – Section 9.2 Corollary Geometry/Trig 2Name: __________________________ Unit 8 GSP Explorations and NotesDate: ___________________________ Tab 2 – Theorem 9-4 Section 9.2 Corollary Theorem 9-4 Conclusion (Corollary): Segments that are tangent to a circle from a point are ____________________. Sketch the diagram: Conclusion (Theorem 9-4): In the same circle or in congruent circles, congruent chords intercept _________________ arcs. Complete Tab 1 Quia Quiz. Example 1: B and C are points of tangency. Classify  ABC by sides: _______________________ m  BAC = 32 m  ABC = ____ m  BCA = ____ BA C Example 2: B and C are points of tangency. x = ________ BA = _______ CA = _______ B A C ½x + 9 4x + 2 Fill in the Measurements: BA BC Fill in the Measurements: AB BC mAGB mBHC Example 1: Find all angle and arc measurements. Example 2: Find all angle and arc measurements concerning circle Q. m  CAB = 40 m  ACB = ________ m  ABC = ________ mAB = 140 mAC = ________ mCB = ________ A C B A B D Q C mAB = 86 mDC = ________ m  DQC = ________ Classify  DQC by sides: ____________ If mBC = 128, then mBAC = _________ Complete Tab 2 Quia Quiz.

2. Tab 3 – Theorem 9-5 Tab 4 – Theorem 9-6 page 2 Theorem 9-5 Theorem 9-6 Conclusion (Theorem 9-5): The diameter that is perpendicular to a chord _____________ the chord and its intercepted arc. To measure the distance between a point and segment, you must measure the ____________________________________ distance. Conclusion (Theorem 9-6): In the same circle or in congruent circles, ______________chords are equally distant from the center. Sketch the diagram: Fill in the Measurements: AF FB mAGC mBHC AD AE FG CB mFHG mCKB Example 1: Find all measurements. Q is the center of the circle. Example 2: Find all measurements. Q is the center of the circle. Example 1: Find all measurements. Q is the center of the circle. R S T M Q P RT = _______ QM = ________ QS = _______ MS = ________ SP = _______ 15 17 mAB = _______ mAC = _______ mCB = _______ m  AQC = ______ m  AQB = ______ m  ABQ = ______ CHALLENGE: If QC = 10, find AB. Q B C A FD mADB = 220 K P Q J N L M Given: KP  QJ; NM  QL QJ = QL = 3 KP = 8 You will need to drawn in QM, QK, and QN to complete this problem. JP = _______ NM = _______ LM = _______ LN = _______ QM = _______ QK = _______ (d) m  QNL = _____________ Complete Tab 3 Quia Quiz. Complete Tab 4 Quia Quiz.

3. Tab 5 – Theorem 9-7 Tab 6 – Section 9.5 corollary 1 page 3 Theorem 9-7 Section 9.5 Corollary 1 Conclusion (Theorem 9-7): The measure of an inscribed angle is equal to ___________ the measure of its intercepted arc. Inscribed Angle: _____________________________________________________ __________________________________________________________________ __________________________________________________________________ Sketch the diagram: m  ABC mADC Example 1: Find all measurements. F H J G 44° 92° 109° m  GFJ = ______ mHJ = ________ mFG = ________ mFGH = _______ mFHG = _______ Conclusion (Corollary 1): Inscribed Angles that intercept the same arc are ___________________________. Sketch the diagram: m  ABD m  ACD mAED Example 1: Find all measurements. A B C D E mAE = 102 m  ABE= _________ m  ACE = _________ m  ADE = _________ mBD = 129 m  BAD = _________ Complete Tab 5 Quia Quiz. Complete Tab 6 Quia Quiz.

4. Tab 7 – Section 9.5 Corollary 2 Tab 8 – Section 9.5 Corollary 3 page 4 Section 9.5 Corollary 3 Section 9.5 Corollary 2 Conclusion (Corollary 2): An angle inscribed inside of a semicircle is _________________________________. Sketch the diagram (include the measurement): Complete: AB is a(n) ____________ ACB is a(n) ___________ Example 1: Find all measurements. AB is a diameter. Example 2: Find all measurements. AB is a diameter. Round all decimal answers to the nearest tenth. B D A AB = 26, AD = 24, DB = _______ m  DBA = ______ m  DAB = _______ mBD = 80 m  ADB = _______ m  ACB = ______ w = _________ x = __________ y = _________ z = ___________ x° y° w°z° Conclusion (Corollary 3): If a quadrilateral is inscribed in a circle, then its opposite angles are ____________________. Sketch the diagram (include the four angle measurements): Find: m  JKL = __________ m  KLM = __________ mMJK = ___________ mJK = _____________ mMLK = ____________ mLMJ = ____________ mLMK = ____________ m  LMJ = 73 m  MJK = 88 mMJ = 102 Example 1: Find all measurements. Complete Tab 7 Quia Quiz. Complete Tab 8 Quia Quiz.

5. Tab 9 – Theorem 9-8 Tab 10 – Theorem 9-10 page 5 Theorem 9-10RULE: Angle = ½(Bigger Arc – Smaller Arc) Theorem 9-8 Conclusion (Theorem 9-8): The measure of an angle formed by a chord and a tangent is equal to ____________ the measure of the intercepted arc. Sketch the diagram: mBGD m  DBC Example 1: Find all measurements. B is a point of tangency. A BC D F m  DBC = 78 mDB = ________ mDFB = _______ m  ABD = ______ Case 1 – Two SecantsCase 2 – Two TangentsCase 3 – A Secant & A Tangent m  1 = __________________m  2 = _________________m  3 = _________________ 3 2 1 Example 1: B is a point of tangency.Example 1: B and C are points of tangency. A B C D m  CAB = 20 mDB = 115 mCB = __________ mCD = __________ mCDB = _________ mBCD = _________ A B C D mBC = 116 mBDC = _________ m  CAB = ________ Complete Tab 9 Quia Quiz. Complete Tab 10 Quia Quiz.

6. Geometry/Trig 2Name: __________________________ Example Problems Answer KeyDate: ___________________________ Tab 1 – Section 9.2 Corollary Tab 2 – Theorem 9-4 Tab 3 – Theorem 9-5 Tab 4 – Theorem 9-6 Tab 5 – Theorem 9-7 Tab 6 – Section 9.5 Corollary 1 Tab 7 – Section 9.5 Corollary 2 Tab 8 – Section 9.5 Corollary 3 Tab 9 – Theorem 9-8Tab 10 – Theorem 9-10 Example 1: Classify  ABC by sides: Isosceles m  ABC = 74 m  BCA = 74 Example 2: x = 2, BA = 10, CA = 10 Example 1: m  ACB = 70 m  ABC = 70 mAC = 140 mCB = 80 Example 2: mDC = 86 m  DQC = 86 Classify  DQC by sides: Isosceles mBAC = 232 Example 1: RT = 30 QM = 8 QS = 17 MS = 9 SP = 34 Example 2: mAB = 140 mAC = 70 mCB = 70 m  AQC = 70 m  AQB = 140 m  ABQ = 20 CHALLENGE: AB = 18.8 Example 1: JP = 4 NM = 8 LM = 4 LN = 4 QM = 5 QK = 5 (d) m  QNL = 36.9 Example 1: m  GFJ = 46 mHJ = 88 mFG = 71 mFGH = 251 mFHG = 289 Example 1: m  ABE= 51 m  ACE = 51 m  ADE = 51 mBD = 129 m  BAD = 64.5 Example 2: AB = 26, AD = 24, DB = 10 m  DBA = 67.4 m  DAB = 22.6 Example 1: m  ADB = 90 m  ACB = 90 w = 40 x = 40 y = 50 z = 50 m  JKL = 107 m  KLM = 92 mMJK = 184 mJK = 82 mMLK = 176 mLMJ = 214 mLMK = 278 Example 1: mDB = 156 mDFB = 204 m  ABD = 102 Example 1: mCB = 75 mCD = 170 mCDB = 285 mBCD = 245 Example 2: mBDC = 244 m  CAB = 64