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Geometry Topics Name: __________________________

Geometry Topics Name: __________________________ Unit 8 GSP Explorations & Notes Date: ___________________________. Tab 1 – Central Angles and Arcs. Tab 1 – Central Angles and Arcs. Rule: The measure of an intercepted arc is __________ to the measure of its central angle.

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Geometry Topics Name: __________________________

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  1. Geometry Topics Name: __________________________ Unit 8 GSP Explorations & Notes Date: ___________________________ Tab 1 – Central Angles and Arcs Tab 1 – Central Angles and Arcs Rule: The measure of an intercepted arc is __________ to the measure of its central angle. Sketch the Diagram: Examples: Use Circle Q. Find: 1) mHB = ________ 2) mBHF = _______ 3) mCBF = _______ 4) mBCD = _______ 5) mBCH = _______ 6) mDFB = _______ 7) mCD = ________ 8) mCDH = _______ H Q 55° B F 32° D C Fill in the measurements: Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 1 Quia Quiz. Complete the quiz. Tab 2 – Tangents and Radii 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. Classify DQAB by angles: ______ What is the length of the radius of Circle Q? ________________ QA = _________ QC = _________ Find QB. ___________________ Find CB. ___________________ Q C A B Fill in the measurements: QA = 10 AB = 24 Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 2 Quia Quiz. Complete the quiz.

  2. Geometry Topics Name: __________________________ Unit 8 GSP Explorations & Notes – page 2 Date: ___________________________ Tab 3 – Tangent Segments from a Point Tab 3 – Tangent Segments from a Point Rule: Segments that are tangent to a circle from a point are _________________. Example 1 (B and C are points of tangency): B Sketch the diagram: Fill in the Measurements: A Classify DBAC by sides? _______________________ mÐBAC = 32 mÐABC = ________ mÐBCA = ________ C Example 2: B B and C are points of tangency. x + 10 x = __________ BA = _________ CA = _________ A 3x + 2 C Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 3 Quia Quiz. Complete the quiz. Tab 4 – Inscribed Angles and Arcs Tab 4 – Inscribed Angles & Arcs Inscribed Angle: ______________________________________________________ ______________________________________________________________________________________________________________________________________ Sketch the Diagram Fill in the Measurements: Rule: The measure of an inscribed angle is equal to ____________ the measure of its intercepted arc. Example: mÐGFJ = ________ mHJ = __________ mFG = __________ mFGH = _________ mFHG = _________ G F 92° 44° J 109° H Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 4 Quia Quiz. Complete the quiz.

  3. Geometry Topics Name: __________________________ Unit 8 GSP Explorations & Notes – page 3 Date: ___________________________ Tab 5 – Inscribed Angles Corollary 1 Tab 5 – Inscribed Angles Corollary 1 Rule: Inscribed Angles that intercept the same arc are ___________________. Sketch the diagram: Fill in the Measurements: Example: mAE = 102 mÐABE = __________ mÐACE = __________ mÐADE = __________ mBD = 129 mÐBAD = __________ 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. Examples: (AB is a diameter of each circle). (Round all decimal answers to the nearest tenth.) Sketch the Diagram (include measurement): mBD = 80 mBC = 80 mÐADB = _____ mÐACB = _____ w = _________ x = __________ y = _________ z = __________ y° w° z° x° AB = 26, AD = 24, DB = ________ mÐDBA = ______ mÐDAB = _____ D Complete: AB is a _______________. ACB is a _______________. B A 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.

  4. Geometry Topics Name: __________________________ Unit 8 GSP Explorations & Notes – page 4 Date: ___________________________ Tab 7 – Inscribed Angles Corollary 3 Tab 7 – Inscribed Angles Corollary 3 Rule: If a quadrilateral is inscribed in a circle, then its opposite angles are _______________. Find: mÐJKL = __________ mÐKLM = __________ mMJK = ___________ mJK = _____________ mMLK = ____________ mLMJ = ____________ mLMK = ____________ Sketch the Diagram (include four angle measurements): Example: mÐLMJ = 73 mÐMJK = 88 mMJ = 102 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 mÐADB = ½(m______ - m______) C E NOTE: mACB + mAEB = _________. D B Example 1: Example 2: B and C are points of tangency. mBC = 116 mBDC = _______ mÐCAB = ______ B B A D D A mBDC = 200 mBC = _________ mÐCAB = _______ C C B and C are points of tangency. Go to http://lschrier.wikispaces.com/geomtopics and find the Tab 8 Quiz. Complete the quiz.

  5. Geometry Topics Name: __________________________ Unit 8 GSP Explorations & Notes Date: ___________________________ Answers to the Example Problems Tab 1 – Central Angles and Arcs Tab 2 – Tangents & Radii 1) mHB = 55 2) mBHF = 180 3) mCBF = 212 4) mBCD = 125 5) mBCH = 305 6) mDFB = 235 7) mCD = 93 8) mCDH = 273 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: Classify DABC by sides. Isosceles mÐBAC = 32 mÐABC = 74 mÐBCA = 74 mÐGFJ = 46 mHJ = 88 mFG = 71 mFGH = 251 mFHG = 289 Example 2: x = 4 BA = 14 CA = 14 Tab 5 – Inscribed Angle Corollary 1 Tab 6 – Inscribed Angle Corollary 2 mÐADB = 90 mÐACB = 90 w = 40 x = 40 y = 50 z = 50 Example 1: mÐABE = 51 mÐACE = 51 mÐADE = 51 mÐBAD = 64.5 Example 2: AB = 26, AD = 24, DB = 10 mÐDBA = 67.4 mÐDAB = 22.6 Tab 7 – Inscribed Angle Corollary 3 Tab 8 – Angles formed by Two Tangents mBDC = 200 mBC = 160 mÐCAB = 20 mÐJKL = 107 mÐKLM = 92 mMJK = 184 mJK = 82 mMLK = 176 mLMJ = 214 mLMK = 296 Example 1: mBC = 116 mBDC = 244 mÐCAB = 64 Example 2:

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