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Geometry Topics Unit 8 GSP Explorations & Notes Name: __________________________ Date: ___________________________ Tab 1 – Central Angles and Arcs Rule: The measure of an intercepted arc is __________ to the measure of its central angle. Tab 1 – Central Angles and Arcs Sketch the Diagram: Examples: Use Circle Q. H Find: 1) mHB = ________ 55° B 3) mCBF = _______ mBQC 4) mBCD = _______ mBKC 5) mBCH = _______ mCQD mFQG 6) mDFB = _______ mCND mFMG 7) mCD = ________ mDQF mGQB 8) mCDH = _______ mDLF mGJB F 32° 2) mBHF = _______ Fill in the measurements: Q C D Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 1 Quia Quiz. Complete the quiz. Tab 2 – Tangents & Radii Rule: If a line is tangent to a circle, then the line is _____________________ to the radius drawn to the point of tangency. Sketch the Diagram: Example – Use circle Q with point of tangency A. Tab 2 – Tangents and Radii Classify DQAB by angles: ______ What is the length of the radius of Circle Q? ________________ Q QA = _________ QC = _________ C Fill in the measurements: mQAB A QA = 10 B AB = 24 Find QB. ___________________ Find CB. ___________________ Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 2 Quia Quiz. Complete the quiz. Geometry Topics Unit 8 GSP Explorations & Notes – page 2 Name: __________________________ Date: ___________________________ Tab 3 – Tangent Segments from a Point Rule: Segments that are tangent to a circle from a point are _________________. Tab 3 – Tangent Segments from a Point Example 1 (B and C are points of tangency): B Sketch the diagram: A Classify DBAC by sides? _______________________ mBAC = 32 C mABC = ________ mBCA = ________ Example 2: Fill in the Measurements: B B and C are points of tangency. x + 10 x = __________ BA A BA = _________ BC C CA = _________ 3x + 2 Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 3 Quia Quiz. Complete the quiz. Tab 4 – Inscribed Angles & Arcs Tab 4 – Inscribed Angles and Arcs Inscribed Angle: ______________________________________________________ ___________________________________________________________________ ___________________________________________________________________ Sketch the Diagram Rule: The measure of an inscribed angle is equal to ____________ the measure of its intercepted arc. Example: mGFJ = ________ G F Fill in the Measurements: mABC mADC mABC mADC 92° 44° mHJ = __________ mFG = __________ J 109° H mFGH = _________ mFHG = _________ Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 4 Quia Quiz. Complete the quiz. Geometry Topics Unit 8 GSP Explorations & Notes – page 3 Name: __________________________ Date: ___________________________ Tab 5 – Inscribed Angles Corollary 1 Rule: Inscribed Angles that intercept the same arc are ___________________. Tab 5 – Inscribed Angles Corollary 1 Sketch the diagram: Example: C B mAE = 102 mABE = __________ mACE = __________ D Fill in the Measurements: mADE = __________ A mABD mACD mBD = 129 E mAED mBAD = __________ Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 5 Quiz. Complete the quiz. Tab 6 – Inscribed Angles Corollary 2 Tab 6 – Inscribed Angles Corollary 2 Rule: An angle inscribed inside of a semicircle is a _____________ angle. Sketch the Diagram (include measurement): Examples: (AB is a diameter of each circle). (Round all decimal answers to the nearest tenth.) C y° A w° x° Q z° mBD = 80 B mBC = 80 mADB = _____ mACB = _____ w = _________ x = __________ y = _________ z = __________ D AB = 26, AD = 24, DB = ________ D Complete: AB is a _______________. ACB is a _______________. B A mDBA = ______ mDAB = _____ HINT: For the angles you have to use trigonometry. Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 6 Quiz. Complete the quiz. Geometry Topics Unit 8 GSP Explorations & Notes – page 4 Name: __________________________ Date: ___________________________ Tab 7 – Inscribed Angles Corollary 3 Rule: If a quadrilateral is inscribed in a circle, then its opposite angles are _______________. Tab 7 – Inscribed Angles Corollary 3 Sketch the Diagram (include four angle measurements): Example: Find: mJKL = __________ M J mKLM = __________ mMJK = ___________ K mJK = _____________ L mLMJ = 73 mMJK = 88 mMLK = ____________ mLMJ = ____________ mMJ = 102 mLMK = ____________ Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 7 Quiz. Complete the quiz. Tab 8 – Angles formed by Two Tangents RULE: Angle = ½(Bigger Arc – Smaller Arc) A and B are points of tangency. A Tab 8 – Angles formed by Two Tangents mADB = ½(m______ - m______) C E D NOTE: mACB + mAEB = _________. B Example 1: B and C are points of tangency. Example 2: B A D mBDC = 200 C mBC = 116 B mBC = _________ mCAB = _______ mBDC = _______ mCAB = ______ D A C B and C are points of tangency. Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 8 Quiz. Complete the quiz. Geometry Topics Unit 8 GSP Explorations & Notes Answers to the Example Problems Name: __________________________ Date: ___________________________ Tab 1 – Central Angles and Arcs 1) mHB = 55 5) mBCH = 305 2) mBHF = 180 6) mDFB = 235 3) mCBF = 212 7) mCD = 93 4) mBCD = 125 8) mCDH = 273 Tab 2 – Tangents & Radii Classify DQAB by angles: Right What is the length of the radius of Circle Q? 10 QA = 10 QC = 10 Find QB. 26 Find CB. 16 Tab 3 – Tangent Segments from a Point Tab 4 – Inscribed Angles and Arcs Example 1: mGFJ = 46 Classify DABC by sides. Isosceles mHJ = 88 mBAC = 32 Example 2: mFG = 71 mABC = 74 x=4 mFGH = 251 mBCA = 74 BA = 14 mFHG = 289 CA = 14 Tab 5 – Inscribed Angle Corollary 1 Tab 6 – Inscribed Angle Corollary 2 Example 1: mADB = 90 mABE = 51 mACE = 51 mADE = 51 mACB = 90 w = 40 x = 40 y = 50 z = 50 Example 2: AB = 26, AD = 24, DB = 10 mBAD = 64.5 mDBA = 67.4 mDAB = 22.6 Tab 7 – Inscribed Angle Corollary 3 mJKL = 107 mMLK = 176 mKLM = 92 mLMJ = 214 mMJK = 184 mLMK = 296 mJK = 82 Tab 8 – Angles formed by Two Tangents Example 1: mBDC = 200 mBC = 160 mCAB = 20 Example 2: mBC = 116 mBDC = 244 mCAB = 64