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Tab 1 – Section 9.2 Corollary

Geometry/Trig 2 Name: __________________________ Unit 8 GSP Explorations and Notes Date: ___________________________. Tab 1 – Section 9.2 Corollary. Section 9.2 Corollary. Conclusion (Corollary): Segments that are tangent to a circle from a point are ____________________.

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Tab 1 – Section 9.2 Corollary

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  1. Geometry/Trig 2 Name: __________________________ Unit 8 GSP Explorations and Notes Date: ___________________________ Tab 1 – Section 9.2 Corollary Section 9.2 Corollary Conclusion (Corollary): Segments that are tangent to a circle from a point are ____________________. Sketch the diagram: Example 1: B and C are points of tangency. Classify DABC by sides: _______________________ mÐBAC = 32 mÐABC = ____ mÐBCA = ____ B A C Example 2: B and C are points of tangency. x = ________ BA = _______ CA = _______ B Fill in the Measurements: ½x + 9 A 4x + 2 C Complete Tab 1 Quia Quiz. Tab 2 – Theorem 9-4 Theorem 9-4 Conclusion (Theorem 9-4): In the same circle or in congruent circles, congruent chords intercept _________________ arcs. Sketch the diagram: Example 1: Find all angle and arc measurements. C mÐCAB = 40 mÐACB = ________ mÐABC = ________ mAB = 140 mAC = ________ mCB = ________ A B Example 2: Find all angle and arc measurements concerning circle Q. Fill in the Measurements: D mAB = 86 mDC = ________ mÐDQC = ________ Classify DDQC by sides: ____________ If mBC = 128, then mBAC = _________ A C Q B Complete Tab 2 Quia Quiz.

  2. Tab 3 – Theorem 9-5 page 2 Theorem 9-5 Conclusion (Theorem 9-5): The diameter that is perpendicular to a chord _____________ the chord and its intercepted arc. Sketch the diagram: Example 1: Find all measurements. Q is the center of the circle. S 15 R T RT = _______ QM = ________ QS = _______ MS = ________ SP = _______ M 17 Q P Fill in the Measurements: Example 2: Find all measurements. Q is the center of the circle. mAB = _______ mAC = _______ mCB = _______mÐAQC = ______ mÐAQB = ______ mÐABQ = ______ CHALLENGE: If QC = 10, find AB. A F D Q C B mADB = 220 Complete Tab 3 Quia Quiz. Theorem 9-6 To measure the distance between a point and segment, you must measure the ____________________________________ distance. Tab 4 – Theorem 9-6 Conclusion (Theorem 9-6): In the same circle or in congruent circles, ______________chords are equally distant from the center. Sketch the diagram: Example 1: Find all measurements. Q is the center of the circle. JP = _______ NM = _______ LM = _______ LN = _______ QM = _______QK = _______ (d) mÐQNL = _____________ K J Q P Fill in the Measurements: L N 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. Complete Tab 4 Quia Quiz.

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

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

  5. Tab 9 – Theorem 9-8 Theorem 9-8 page 5 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: Example 1: Find all measurements. B is a point of tangency. mÐDBC = 78 mDB = ________ mDFB = _______ mÐABD = ______ D F A B C Complete Tab 9Quia Quiz. Tab 10 – Theorem 9-10 Theorem 9-10 RULE: Angle = ½(Bigger Arc – Smaller Arc) Case 1 – Two Secants Case 2 – Two Tangents Case 3 – A Secant & A Tangent 1 3 2 mÐ1 = __________________ mÐ2 = _________________ mÐ3 = _________________ Example 1: B is a point of tangency. Example 1: B and C are points of tangency. D B mÐCAB = 20 mDB = 115 mCB = __________ mCD = __________ mCDB = _________mBCD = _________ C D A A B C mBC = 116 mBDC = _________ mÐCAB = ________ Complete Tab 10 Quia Quiz.

  6. Geometry/Trig 2 Name: __________________________ Example Problems Answer Key Date: ___________________________ Tab 2 – Theorem 9-4 Tab 1 – Section 9.2 Corollary Example 1: mÐACB = 70 mÐABC = 70 mAC = 140 mCB = 80 Example 1: Classify DABC by sides: Isosceles mÐABC = 74 mÐBCA = 74 Example 2: x = 2, BA = 10, CA = 10 Example 2: mDC = 86 mÐDQC = 86 Classify DDQC by sides: Isosceles mBAC = 232 Tab 4 – Theorem 9-6 Tab 3 – Theorem 9-5 Example 1: JP = 4 NM = 8 LM = 4 LN = 4 QM = 5 QK = 5 (d) mÐQNL = 36.9 Example 1: RT = 30 QM = 8 QS = 17 MS = 9 SP = 34 Example 2: mAB = 140 mAC = 70 mCB = 70 mÐAQC = 70 mÐAQB = 140 mÐABQ = 20 CHALLENGE: AB = 18.8 Tab 6 – Section 9.5 Corollary 1 Tab 5 – Theorem 9-7 Example 1: mÐGFJ = 46 mHJ = 88 mFG = 71 mFGH = 251 mFHG = 289 Example 1: mÐABE= 51 mÐACE = 51 mÐADE = 51 mBD = 129 mÐBAD = 64.5 Tab 8 – Section 9.5 Corollary 3 Tab 7 – Section 9.5 Corollary 2 Example 1: mÐADB = 90 mÐACB = 90 w = 40 x = 40 y = 50 z = 50 mÐJKL= 107 mÐKLM = 92 mMJK = 184 mJK = 82 mMLK = 176 mLMJ = 214 mLMK = 278 Example 2: AB = 26, AD = 24, DB = 10 mÐDBA = 67.4 mÐDAB = 22.6 Tab 9 – Theorem 9-8 Tab 10 – Theorem 9-10 Example 1: mDB = 156 mDFB = 204 mÐABD = 102 Example 1: mCB = 75 mCD = 170 mCDB = 285mBCD = 245 Example 2: mBDC = 244 mÐCAB = 64

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