Page 1 Central Angles & Arc Measures
|
|
- Arron Adams
- 6 years ago
- Views:
Transcription
1 Geometry/Trig Unit 8 ll bout ircles! Name: ate: Page 1 entral ngles & rc Measures Example 1: JK is a diameter of ircle. Name two examples for each: K Minor rc:, Major rc:, M Semicircle:, Name Pair of djacent rcs:, J L Example 2: G is the center of the circle. G ^ m = 75 m = m = 2. m = 3. m G = 4. m G = 5. m = 6. m G = 7. m G = 8. m = 9. m = 10. m = 11. m = 12. m = 13. m = 14. m = 15. mg = 16. m = 17. mg = 18. m = 19. mg = 20. mg =
2 Page 2 Problem Set 1 irections: Solve for each indicated variable or segment. is the center of each circle. 1. z refers to an 2. = 8 arc measure. z y x x = y = z = 3. = = = y x 130 m = 120 x z z y z refers to an arc measure. y and z refers to arc measures. x = y = z = x = y = z = 5. m = m 1 = m 2 = Textbook Practice: p. 341 E #1-13; p WE #1-6, 10, 11
3 Page 3 Example Tab Theorem 9-1 Sketch the diagram: Observations: ill in the Measurements: m PR onclusion (Theorem 9-1): If a line is tangent to a circle, then the line is to the radius drawn to the point of tangency. Example 1: Given ircle with a radius length of 5. is a point of tangency. = 5 3. Example 2: Given ircle with a radius length of 7. is a point of tangency. = 24. G ind: = m = m = Example 3: Given JK is a diameter and KL is a tangent. The radius of the circle is 8. J ind: = G = G = m = Is G the midpoint of? mg = UI UIZ EXMPLE Given ircle and is a point of tangency. = 8 = 17 K 45 L ind: JK = JL = KL = Example uia uiz: / 5
4 Page 4 Tab 1 orollary of Theorem 9-1 Sketch the diagram: Observations: ill in the Measurements: onclusion (orollary to Theorem 9-1): Segments that are tangent to a circle from a point are. Example 1: and are points of tangency. lassify by sides: m = 32 m = m = Example 2: and are points of tangency. x = ½x + 9 = = Example 3: Points J, K, L, and M are points of tangency. ind the perimeter of quadrilateral. J K J = 4, K = 7, L = 3, M = 5 K 4x + 2 UI UIZ 1 L Points K and J are points of Tangency. J KL = 7; KJ = 6; m LKJ = 70 M L Perimeter: uia uiz 1: / 4
5 Page 5 Problem Set 2 irections: ind the value of each indicated variable and measure. 1. is a tangent of ircle. 2. and are tangents to the circle. 8 3 = 2x + 2 = 4x + 8 = 7x + 2 = 5x + 1 G x = = = m = G = m = = x = = = 3. P,, R, and S are points of tangency. P 4. and are tangent segments. m = S 9 9 R ind the perimeter of uadrilateral. = m = Textbook Practice: p. 335 WE #1-5
6 Page 6 Tab 2 Theorem 9-4 Sketch the diagram: ill in Measurements: mg mh Observations: onclusion (Theorem 9-4): In the same circle or in congruent circles, congruent chords intercept arcs. Example 1: ind all angle and arc measurements. m = 40 m = m = m = 140 m = m = Example 2: ind all angle and arc measurements concerning circle. m = 86 m = m = lassify by sides: If m = 128, then m = UI UIZ 2 = 9 = 9 uia uiz 2: / 4 m = 131 m = 33
7 Page 7 Tab 3 Theorem 9-5 Sketch the diagram: ill in Measurements: mg mh Observations: onclusion (Theorem 9-5): The diameter that is perpendicular to a chord the chord and its intercepted arc. Example 1: ind all measurements. is the center of the circle. S RT = R 15 T M 17 S = M = MS = SP = P Example 2: ind all measurements. is the center of the circle. m = m = m = m = m = m = m = 220 HLLENGE: If = 10, find. UI UIZ 3 S ^ RP S is a diameter. RP = 18 mrs = 70 R T P uia uiz 3: / 6 S
8 Page 8 Tab 4 Theorem 9-6 Sketch the diagram: To measure the distance between a point and segment, you must measure the distance. ill in Measurements: E G mhg mk Observations: onclusion (Theorem 9-6): In the same circle or in congruent circles, chords are equally distant from the center. Example 1: ind all measurements. is the center of the circle. K JP = NM = J LM = LN = P M = K = N L M m NL = Given: KP ^ J; NM ^ L J = L = 3 KP = 8 E UI UIZ 4 E ^ G ^ G = 8 m = 106 = 3 E = 3 You will need to drawn in M, K, and N to complete this problem. uia uiz 4: / 3
9 Page 9 Problem Set 3 omplete each problem from the Written Exercises on page 347. raw and label a diagram for each problem
10 Page 10 Tab 5 Theorem 9-7 & orollaries 1 & 2 Sketch the diagram: Recall Inscribed ngle: _ m m m m Observations: _ onclusion (Theorem 9-7): The measure of an inscribed angle is equal to the measure of its intercepted arc. orollary 1: Inscribed ngles that intercept the same arc are. orollary 2: n angle inscribed inside of a semicircle is. Example 1: ind all measurements. G J m GJ = mhj = Example 2: ind all measurements. me = 102 m E= 109 mg = m E = H mgh = m E = mhg = E m = 129 m = Example 3: ind all measurements. is a diameter. Round all decimal answers to the nearest tenth. N UI UIZ 5 M P iagram 2 = 26, = 24, = m = m = iagram 1 mmp = 122; mmn = 40 is a diameter; = 6; = 10 uia uiz 5: / 7
11 Page 11 Tab 6 Theorem 9-7 orollary 3 Sketch the diagram (include the four angle measurements): Observations: onclusion (orollary 3): If a quadrilateral is inscribed in a circle, then its opposite angles are. Example 1: ind all measurements. Given: M m LMJ = 73 J m MJK = 88 mmj = 102 K L ind: m JKL = m KLM = mmjk = mjk = mmlk = mlmj = mlmk = Example 2: UI UIZ 6 R S T Given: uadrilateral is inscribed in ircle. = 8 and = 15. ind each measure: iameter Length = Radius Length = m RST = 102 m SRP = 65 P m = uia uiz 6: / 4
12 Page 12 Problem Set 4 irections: ind each indicated measure X is the center of the circle. G 75 X 120 mg = m = m G = N is a diameter J 100 K P 40 N M L m JMK = m JLK = 5. R 6. m NP = mnp = S T m SRT = m = m = Textbook Practice: p. 353 E #4, 5, 6, 9; p. 354 WE #1-4, 6
13 Page 13 Tab 7 Theorem 9-8 Sketch the diagram: Observations: onclusion (Theorem 9-8): mg m m mg The measure of an angle formed by a chord and a tangent is equal to the measure of the intercepted arc. Example 1: ind all indicated measurements. is a point of tangency. Example 2: ind all indicated measurements. is a point of tangency. m = 78 x 72 m = m = m = x = m = m = UI UIZ 7 N M K is a point of tangency. m MKL = 74 J K L uia uiz 7: / 3
14 Page 14 Tab 8 Theorem 9-10 RULE: ngle = ½(igger rc Smaller rc) ase 1 Two Secants ase 2 Two Tangents ase 3 Secant & Tangent m 1 = m 2 = m 3 = Example 1: is a point of tangency. Example 2: and are points of tangency. m = 20 m = 115 m = m = m = m = m = 116 m = m = UI UIZ 8 is a point of tangency. m = 120 m = 50 G H uia uiz 8: / 4
15 Page 15 Problem Set 5 omplete each problem from the lassroom Exercises on pages raw an label a diagram for each Textbook Practice: p. 353 E #7, 8; p. 354 WE #5, 7, 8, 9; p. 360 #15-21
16 Page 16 nswers to Examples Example Tab Theorem 9-1 Example 1: = 10 m = 60 m = 30 Example 2: = 25, G = 7, G = 18 m = 73.7 mg = 73.7 Is G the midpoint of? No Example 3: JK = 16, KL = 16, JL = 16 2 Tab 1 orollary to Theorem 9-1 Example 1: lassify by sides: Isosceles m = 74 m = 74 Example 2: x = 2, = 10, = 10 Example 3: Perimeter = 38 Tab 2 Theorem 9-4 Example 1: m = 70 m = 70 m = 140 m = 80 Example 2: m = 86 m = 86 lassify by sides: Isosceles m = 232 Tab 3 Theorem 9-5 Example 1: RT = 30 M = 8 S = 17 MS = 9 SP = 34 Example 2: m = 140 m = 70 m = 70 m = 70 m = 140 m = 20 HLLENGE: = 18.8 Tab 4 Theorem 9-6 Example 1: JP = 4 NM = 8 LM = 4 LN = 4 M = 5 K = 5 m NL = 36.9 Tab 5 Theorem 9-7 & orollaries 1 & 2 Example 1: m GJ = 46 mhj = 88 mg = 71 mgh = 251 mhg = 289 Example 2: m E= 51 m E = 51 m E = 51 m = 129 m = 64.5 Example 3: = 26, = 24, = 10 m = 67.4 m = 22.6 Tab 6 Section 9.5 orollary 3 Example 1: m JKL = 107 mmlk = 176 m KLM = 92 mlmj = 214 mmjk = 184 mlmk = 296 mjk = 82 Example 2: iameter Length = 17 Radius Length = 17 2 m = 28.1 Tab 7 Theorem 9-8 Example 1: m = 156 m = 204 m = 102 Example 2: x = 108 m = 108 m = 54 Tab 8 Theorem 9-10 Example 1: m = 75 m = 170 m = 285 m = 245 Example 2: m = 244 m = 64
Honors Geometry Circle Investigation - Instructions
Honors Geometry ircle Investigation - Instructions 1. On the first circle a. onnect points and O with a line segment. b. onnect points O and also. c. Measure O. d. Estimate the degree measure of by using
More informationRiding a Ferris Wheel
Lesson.1 Skills Practice Name ate iding a Ferris Wheel Introduction to ircles Vocabulary Identify an instance of each term in the diagram. 1. center of the circle 6. central angle T H I 2. chord 7. inscribed
More informationExample 1: Finding angle measures: I ll do one: We ll do one together: You try one: ML and MN are tangent to circle O. Find the value of x
Ch 1: Circles 1 1 Tangent Lines 1 Chords and Arcs 1 3 Inscribed Angles 1 4 Angle Measures and Segment Lengths 1 5 Circles in the coordinate plane 1 1 Tangent Lines Focused Learning Target: I will be able
More informationGeometry: A Complete Course
eometry: omplete ourse with rigonometry) odule - tudent Worket Written by: homas. lark Larry. ollins 4/2010 or ercises 20 22, use the diagram below. 20. ssume is a rectangle. a) f is 6, find. b) f is,
More information( ) Chapter 10 Review Question Answers. Find the value of x mhg. m B = 1 2 ( 80 - x) H x G. E 30 = 80 - x. x = 50. Find m AXB and m Y A D X 56
hapter 10 Review Question nswers 1. ( ) Find the value of mhg 30 m = 1 2 ( 30) = 15 F 80 m = 1 2 ( 80 - ) H G E 30 = 80 - = 50 2. Find m X and m Y m X = 1 120 + 56 2 ( ) = 88 120 X 56 Y m Y = 1 120-56
More informationReview for Grade 9 Math Exam - Unit 8 - Circle Geometry
Name: Review for Grade 9 Math Exam - Unit 8 - ircle Geometry Date: Multiple hoice Identify the choice that best completes the statement or answers the question. 1. is the centre of this circle and point
More informationSkills Practice Skills Practice for Lesson 11.1
Skills Practice Skills Practice for Lesson.1 Name ate Riding a Ferris Wheel Introduction to ircles Vocabulary Identify an instance of each term in the diagram. 1. circle X T 2. center of the circle H I
More informationArcs and Inscribed Angles of Circles
Arcs and Inscribed Angles of Circles Inscribed angles have: Vertex on the circle Sides are chords (Chords AB and BC) Angle ABC is inscribed in the circle AC is the intercepted arc because it is created
More informationSM2H Unit 6 Circle Notes
Name: Period: SM2H Unit 6 Circle Notes 6.1 Circle Vocabulary, Arc and Angle Measures Circle: All points in a plane that are the same distance from a given point, called the center of the circle. Chord:
More informationC=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle
10.1 Circles and Circumference Chapter 10 Circles Circle the locus or set of all points in a plane that are A equidistant from a given point, called the center When naming a circle you always name it by
More informationMth 076: Applied Geometry (Individualized Sections) MODULE FOUR STUDY GUIDE
Mth 076: pplied Geometry (Individualized Sections) MODULE FOUR STUDY GUIDE INTRODUTION TO GEOMETRY Pick up Geometric Formula Sheet (This sheet may be used while testing) ssignment Eleven: Problems Involving
More informationStudy Guide. Exploring Circles. Example: Refer to S for Exercises 1 6.
9 1 Eploring ircles A circle is the set of all points in a plane that are a given distance from a given point in the plane called the center. Various parts of a circle are labeled in the figure at the
More informationSolve problems involving tangents to a circle. Solve problems involving chords of a circle
8UNIT ircle Geometry What You ll Learn How to Solve problems involving tangents to a circle Solve problems involving chords of a circle Solve problems involving the measures of angles in a circle Why Is
More informationUnit 10 Geometry Circles. NAME Period
Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference
More informationRiding a Ferris Wheel. Students should be able to answer these questions after Lesson 10.1:
.1 Riding a Ferris Wheel Introduction to ircles Students should be able to answer these questions after Lesson.1: What are the parts of a circle? How are the parts of a circle drawn? Read Question 1 and
More informationradii: AP, PR, PB diameter: AB chords: AB, CD, AF secant: AG or AG tangent: semicircles: ACB, ARB minor arcs: AC, AR, RD, BC,
h 6 Note Sheets L Shortened Key Note Sheets hapter 6: iscovering and roving ircle roperties eview: ircles Vocabulary If you are having problems recalling the vocabulary, look back at your notes for Lesson
More informationCircles. II. Radius - a segment with one endpoint the center of a circle and the other endpoint on the circle.
Circles Circles and Basic Terminology I. Circle - the set of all points in a plane that are a given distance from a given point (called the center) in the plane. Circles are named by their center. II.
More information10-1 Study Guide and Intervention
opyright Glencoe/McGraw-Hill, a division of he McGraw-Hill ompanies, Inc. NM I 10-1 tudy Guide and Intervention ircles and ircumference arts of ircles circle consists of all points in a plane that are
More informationTangent Lines Unit 10 Lesson 1 Example 1: Tell how many common tangents the circles have and draw them.
Tangent Lines Unit 10 Lesson 1 EQ: How can you verify that a segment is tangent to a circle? Circle: Center: Radius: Chord: Diameter: Secant: Tangent: Tangent Lines Unit 10 Lesson 1 Example 1: Tell how
More informationWhat is the longest chord?.
Section: 7-6 Topic: ircles and rcs Standard: 7 & 21 ircle Naming a ircle Name: lass: Geometry 1 Period: Date: In a plane, a circle is equidistant from a given point called the. circle is named by its.
More informationObjectives To find the measure of an inscribed angle To find the measure of an angle formed by a tangent and a chord
1-3 Inscribed ngles ommon ore State Standards G-.. Identify and describe relationships among inscribed angles, radii, and chords. lso G-..3, G-..4 M 1, M 3, M 4, M 6 bjectives To find the measure of an
More information( ) Find the value of x mhg. H x G. Find m AXB and m Y A D X 56. Baroody Page 1 of 18
1. ( ) Find the value of x mhg 30 F 80 H x G E 2. Find m X and m Y 120 X 56 Y aroody age 1 of 18 3. Find mq X 70 30 Y Q 4. Find the radius of a circle in which a 48 cm. chord is 8 cm closer to the center
More informationChapter 12 Practice Test
hapter 12 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. ssume that lines that appear to be tangent are tangent. is the center of the circle.
More informationIndicate whether the statement is true or false.
PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.
More information2 Explain 1 Proving the Intersecting Chords Angle Measure Theorem
xplain 1 Proving the Intersecting hords ngle easure Theorem In the xplore section, you discovered the effects that line segments, such as chords and secants, have on angle measures and their intercepted
More information1. Draw and label a diagram to illustrate the property of a tangent to a circle.
Master 8.17 Extra Practice 1 Lesson 8.1 Properties of Tangents to a Circle 1. Draw and label a diagram to illustrate the property of a tangent to a circle. 2. Point O is the centre of the circle. Points
More informationDO NOW #1. Please: Get a circle packet
irclengles.gsp pril 26, 2013 Please: Get a circle packet Reminders: R #10 due Friday Quiz Monday 4/29 Quiz Friday 5/3 Quiz Wednesday 5/8 Quiz Friday 5/10 Initial Test Monday 5/13 ctual Test Wednesday 5/15
More informationAssignment. Riding a Ferris Wheel Introduction to Circles. 1. For each term, name all of the components of circle Y that are examples of the term.
ssignment ssignment for Lesson.1 Name Date Riding a Ferris Wheel Introduction to ircles 1. For each term, name all of the components of circle Y that are examples of the term. G R Y O T M a. hord GM, R,
More informationChapter-wise questions
hapter-wise questions ircles 1. In the given figure, is circumscribing a circle. ind the length of. 3 15cm 5 2. In the given figure, is the center and. ind the radius of the circle if = 18 cm and = 3cm
More informationLesson 1.7 circles.notebook. September 19, Geometry Agenda:
Geometry genda: Warm-up 1.6(need to print of and make a word document) ircle Notes 1.7 Take Quiz if you were not in class on Friday Remember we are on 1.7 p.72 not lesson 1.8 1 Warm up 1.6 For Exercises
More informationReplacement for a Carpenter s Square
Lesson.1 Skills Practice Name Date Replacement for a arpenter s Square Inscribed and ircumscribed Triangles and Quadrilaterals Vocabulary nswer each question. 1. How are inscribed polygons and circumscribed
More informationIntroduction Circle Some terms related with a circle
141 ircle Introduction In our day-to-day life, we come across many objects which are round in shape, such as dials of many clocks, wheels of a vehicle, bangles, key rings, coins of denomination ` 1, `
More informationGeo - CH11 Practice Test
Geo - H11 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Identify the secant that intersects ñ. a. c. b. l d. 2. satellite rotates 50 miles
More informationReady To Go On? Skills Intervention 11-1 Lines That Intersect Circles
Name ate lass STION 11 Ready To Go On? Skills Intervention 11-1 Lines That Intersect ircles ind these vocabulary words in Lesson 11-1 and the Multilingual Glossary. Vocabulary interior of a circle exterior
More informationAnswers. Chapter10 A Start Thinking. and 4 2. Sample answer: no; It does not pass through the center.
hapter10 10.1 Start Thinking 6. no; is not a right triangle because the side lengths do not satisf the Pthagorean Theorem (Thm. 9.1). 1. (3, ) 7. es; is a right triangle because the side lengths satisf
More informationGeometry Honors Homework
Geometry Honors Homework pg. 1 12-1 Practice Form G Tangent Lines Algebra Assume that lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. 2. 3. The circle
More informationName Date Period. Notes - Tangents. 1. If a line is a tangent to a circle, then it is to the
Name ate Period Notes - Tangents efinition: tangent is a line in the plane of a circle that intersects the circle in eactly one point. There are 3 Theorems for Tangents. 1. If a line is a tangent to a
More informationFind the area of the triangle. You try: D C. Determine whether each of the following statements is true or false. Solve for the variables.
lameda USD Geometr enchmark Stud Guide ind the area of the triangle. 9 4 5 D or all right triangles, a + b c where c is the length of the hpotenuse. 5 4 a + b c 9 + b 5 + b 5 b 5 b 44 b 9 he area of a
More informationChords and Arcs. Objectives To use congruent chords, arcs, and central angles To use perpendicular bisectors to chords
- hords and rcs ommon ore State Standards G-.. Identify and describe relationships among inscribed angles, radii, and chords. M, M bjectives To use congruent chords, arcs, and central angles To use perpendicular
More information0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?
0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30
More informationName Grp Pd Date. Circles Test Review 1
ircles est eview 1 1. rc 2. rea 3. entral ngle 4. hord 5. ircumference 6. Diameter 7. Inscribed 8. Inscribed ngle 9. Intercepted rc 10. Pi 11. adius 12. ector 13. emicircle 14. angent 15. πr 2 16. 2πr
More informationUsing Properties of Segments that Intersect Circles
ig Idea 1 H UY I I Using roperties of egments that Intersect ircles or Your otebook You learned several relationships between tangents, secants, and chords. ome of these relationships can help you determine
More informationAssignment. Riding a Ferris Wheel Introduction to Circles. 1. For each term, name all of the components of circle Y that are examples of the term.
ssignment ssignment for Lesson.1 Name Date Riding a Ferris Wheel Introduction to Circles 1. For each term, name all of the components of circle Y that are examples of the term. G R Y O T M a. Chord b.
More informationUNIT OBJECTIVES. unit 9 CIRCLES 259
UNIT 9 ircles Look around whatever room you are in and notice all the circular shapes. Perhaps you see a clock with a circular face, the rim of a cup or glass, or the top of a fishbowl. ircles have perfect
More informationChapter 10. Properties of Circles
Chapter 10 Properties of Circles 10.1 Use Properties of Tangents Objective: Use properties of a tangent to a circle. Essential Question: how can you verify that a segment is tangent to a circle? Terminology:
More information10.3 Start Thinking Warm Up Cumulative Review Warm Up
10.3 tart hinking etermine if the statement is always true, sometimes true, or never true. plain your reasoning. 1. chord is a diameter. 2. diameter is a chord. 3. chord and a radius have the same measure.
More informationPre-Test. Use the following figure to answer Questions 1 through 6. B C. 1. What is the center of the circle? The center of the circle is point G.
Pre-Test Name Date Use the following figure to answer Questions 1 through 6. A B C F G E D 1. What is the center of the circle? The center of the circle is point G. 2. Name a radius of the circle. A radius
More informationIncoming Magnet Precalculus / Functions Summer Review Assignment
Incoming Magnet recalculus / Functions Summer Review ssignment Students, This assignment should serve as a review of the lgebra and Geometry skills necessary for success in recalculus. These skills were
More informationAnswer Key. 9.1 Parts of Circles. Chapter 9 Circles. CK-12 Geometry Concepts 1. Answers. 1. diameter. 2. secant. 3. chord. 4.
9.1 Parts of Circles 1. diameter 2. secant 3. chord 4. point of tangency 5. common external tangent 6. common internal tangent 7. the center 8. radius 9. chord 10. The diameter is the longest chord in
More informationGeometry H Ch. 10 Test
Geometry H Ch. 10 est 1. In the diagram, point is a point of tangency,, and. What is the radius of? M N J a. 76 c. 72 b. 70 d. 64 2. In the diagram, is tangent to at, is tangent to at,, and. Find the value
More informationCircles in Neutral Geometry
Everything we do in this set of notes is Neutral. Definitions: 10.1 - Circles in Neutral Geometry circle is the set of points in a plane which lie at a positive, fixed distance r from some fixed point.
More informationCircles-Tangent Properties
15 ircles-tangent roperties onstruction of tangent at a point on the circle. onstruction of tangents when the angle between radii is given. Tangents from an external point - construction and proof Touching
More informationARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS.
ARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS. A B X Z Y A MINOR arc is LESS than 1/2 way around the circle. A MAJOR arc is MORE than 1/2 way around
More informationUse Properties of Tangents
6.1 Georgia Performance Standard(s) MM2G3a, MM2G3d Your Notes Use Properties of Tangents Goal p Use properties of a tangent to a circle. VOULRY ircle enter Radius hord iameter Secant Tangent Example 1
More informationName. 9. Find the diameter and radius of A, B, and C. State the best term for the given figure in the diagram.
Name LESSON 10.1 State the best term for the given figure in the diagram. 9. Find the diameter and radius of A, B, and C. 10. Describe the point of intersection of all three circles. 11. Describe all the
More informationChapter 19 Exercise 19.1
hapter 9 xercise 9... (i) n axiom is a statement that is accepted but cannot be proven, e.g. x + 0 = x. (ii) statement that can be proven logically: for example, ythagoras Theorem. (iii) The logical steps
More information0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.
0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,
More informationReteaching , or 37.5% 360. Geometric Probability. Name Date Class
Name ate lass Reteaching Geometric Probability INV 6 You have calculated probabilities of events that occur when coins are tossed and number cubes are rolled. Now you will learn about geometric probability.
More informationChapter 1. Some Basic Theorems. 1.1 The Pythagorean Theorem
hapter 1 Some asic Theorems 1.1 The ythagorean Theorem Theorem 1.1 (ythagoras). The lengths a b < c of the sides of a right triangle satisfy the relation a 2 + b 2 = c 2. roof. b a a 3 2 b 2 b 4 b a b
More informationNew Jersey Center for Teaching and Learning. Progressive Mathematics Initiative
Slide 1 / 150 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students
More informationName two radii in Circle E.
A C E B D Name two radii in Circle E. Unit 4: Prerequisite Terms A C E B D ECandED Unit 4: Prerequisite Terms A C E B D Name all chords in Circle E. Unit 4: Prerequisite Terms A C E B D AD, CD, AB Unit
More informationGeometry: A Complete Course
Geometry: omplete ourse (with Trigonometry) Module - Student WorkText Written by: Thomas E. lark Larry E. ollins Geometry: omplete ourse (with Trigonometry) Module Student Worktext opyright 2014 by VideotextInteractive
More informationMath 9 Unit 8: Circle Geometry Pre-Exam Practice
Math 9 Unit 8: Circle Geometry Pre-Exam Practice Name: 1. A Ruppell s Griffon Vulture holds the record for the bird with the highest documented flight altitude. It was spotted at a height of about 11 km
More informationEvaluate: Homework and Practice
valuate: Homework and Practice Identify the chord (s), inscribed angle (s), and central angle (s) in the figure. The center of the circles in xercises 1, 2, and 4 is. Online Homework Hints and Help xtra
More information10.6 Find Segment Lengths
10. Find Segment Lengths in ircles Goal p Find segment lengths in circles. Your Notes VOULRY Segments of a chord Secant segment Eternal segment THEOREM 10.14: SEGMENTS OF HORS THEOREM If two chords intersect
More information( ) ( ) Geometry Team Solutions FAMAT Regional February = 5. = 24p.
. A 6 6 The semi perimeter is so the perimeter is 6. The third side of the triangle is 7. Using Heron s formula to find the area ( )( )( ) 4 6 = 6 6. 5. B Draw the altitude from Q to RP. This forms a 454590
More informationPark Forest Math Team. Meet #4. Geometry. Self-study Packet
Park Forest Math Team Meet #4 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. : ngle measures in plane figures including supplements and complements 3. Number Theory:
More information11. Concentric Circles: Circles that lie in the same plane and have the same center.
Circles Definitions KNOW THESE TERMS 1. Circle: The set of all coplanar points equidistant from a given point. 2. Sphere: The set of all points equidistant from a given point. 3. Radius of a circle: The
More informationb) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals Converse d) Opposite sides Parallel and Congruent Theorem
Chapter 7 1. State which theorem you can use to show that the quadrilateral is a parallelogram. a) Parallelogram Opposite Angles Converse b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals
More informationClick on a topic to go to that section. Euclid defined a circle and its center in this way: Euclid defined figures in this way:
lide 1 / 59 lide / 59 New Jersey enter for eaching and Learning Progressive Mathematics Initiative his material is made freely available at www.njctl.org and is intended for the non-commercial use of students
More informationLesson 12.1 Skills Practice
Lesson 12.1 Skills Practice Introduction to ircles ircle, Radius, and iameter Vocabulary efine each term in your own words. 1. circle circle is a collection of points on the same plane equidistant from
More informationSo, PQ is about 3.32 units long Arcs and Chords. ALGEBRA Find the value of x.
ALGEBRA Find the value of x. 1. Arc ST is a minor arc, so m(arc ST) is equal to the measure of its related central angle or 93. and are congruent chords, so the corresponding arcs RS and ST are congruent.
More information15.3 Tangents and Circumscribed Angles
Name lass ate 15.3 Tangents and ircumscribed ngles Essential uestion: What are the key theorems about tangents to a circle? esource Locker Explore Investigating the Tangent-adius Theorem tangent is a line
More informationTopic 4 Congruent Triangles PAP
opic 4 ongruent riangles PP Name: Period: eacher: 1 P a g e 2 nd Six Weeks 2015-2016 MONY USY WNSY HUSY FIY Oct 5 6 7 8 9 3.4/3.5 Slopes, writing and graphing equations of a line HW: 3.4/3.5 Slopes, writing
More informationGeometry: A Complete Course
Geometry: omplete ourse (with Trigonometry) Module Progress Tests Written by: Larry E. ollins Geometry: omplete ourse (with Trigonometry) Module - Progress Tests opyright 2014 by VideotextInteractive Send
More informationTheorem 1.2 (Converse of Pythagoras theorem). If the lengths of the sides of ABC satisfy a 2 + b 2 = c 2, then the triangle has a right angle at C.
hapter 1 Some asic Theorems 1.1 The ythagorean Theorem Theorem 1.1 (ythagoras). The lengths a b < c of the sides of a right triangle satisfy the relation a + b = c. roof. b a a 3 b b 4 b a b 4 1 a a 3
More information0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?
0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle
More informationTo construct the roof of a house, an architect must determine the measures of the support beams of the roof.
Metric Relations Practice Name : 1 To construct the roof of a house, an architect must determine the measures of the support beams of the roof. m = 6 m m = 8 m m = 10 m What is the length of segment F?
More informationCircles. 1. In the accompanying figure, the measure of angle AOB is 50. Find the measure of inscribed angle ACB.
ircles Name: Date: 1. In the accompanying figure, the measure of angle AOB is 50. Find the measure of inscribed angle AB. 4. In the accompanying diagram, P is tangent to circle at and PAB is a secant.
More informationCircle-Chord properties
14 ircle-hord properties onstruction of a chord of given length. Equal chords are equidistant from the centre. ngles in a segment. ongrue nt circles and concentric circles. onstruction of congruent and
More informationGeometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems
Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary
More informationGeometry 1.0 Errata October 15, 2012
Geometry Errors on Current Printing Geometry.0 Errata October 5, 202 Lesson 23 #2: Answer key should say if two angles are complementary to the same angle they are congruent. The solution should say this
More information0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.
0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD
More informationName. Chapter 12: Circles
Name Chapter 12: Circles Chapter 12 Calendar Sun Mon Tue Wed Thu Fri Sat May 13 12.1 (Friday) 14 Chapter 10/11 Assessment 15 12.2 12.1 11W Due 16 12.3 12.2 HW Due 17 12.1-123 Review 12.3 HW Due 18 12.1-123
More informationName: GEOMETRY: EXAM (A) A B C D E F G H D E. 1. How many non collinear points determine a plane?
GMTRY: XM () Name: 1. How many non collinear points determine a plane? ) none ) one ) two ) three 2. How many edges does a heagonal prism have? ) 6 ) 12 ) 18 ) 2. Name the intersection of planes Q and
More information0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
More informationGCSE METHODS IN MATHEMATICS
Q Qualifications GCSE METHODS IN MTHEMTICS Linked Pair Pilot Specification (9365) ssessment Guidance Our specification is published on our website (www.aqa.org.uk). We will let centres know in writing
More informationMT - MATHEMATICS (71) GEOMETRY - PRELIM II - PAPER - 6 (E)
04 00 Seat No. MT - MTHEMTIS (7) GEOMETRY - PRELIM II - (E) Time : Hours (Pages 3) Max. Marks : 40 Note : ll questions are compulsory. Use of calculator is not allowed. Q.. Solve NY FIVE of the following
More informationCircles. Exercise 9.1
9 uestion. Exercise 9. How many tangents can a circle have? Solution For every point of a circle, we can draw a tangent. Therefore, infinite tangents can be drawn. uestion. Fill in the blanks. (i) tangent
More informationGeometry Honors Final Exam Review June 2018
Geometry Honors Final Exam Review June 2018 1. Determine whether 128 feet, 136 feet, and 245 feet can be the lengths of the sides of a triangle. 2. Casey has a 13-inch television and a 52-inch television
More informationMAHESH TUTORIALS. GEOMETRY Chapter : 1, 2, 6. Time : 1 hr. 15 min. Q.1. Solve the following : 3
S.S.C. Test - III Batch : SB Marks : 0 Date : MHESH TUTORILS GEOMETRY Chapter : 1,, 6 Time : 1 hr. 15 min..1. Solve the following : (i) The dimensions of a cuboid are 5 cm, 4 cm and cm. Find its volume.
More information10-3 Arcs and Chords. ALGEBRA Find the value of x.
ALGEBRA Find the value of x. 1. Arc ST is a minor arc, so m(arc ST) is equal to the measure of its related central angle or 93. and are congruent chords, so the corresponding arcs RS and ST are congruent.
More informationTHEOREM 10.3 B C In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
10.3 Your Notes pply Properties of hords oal p Use relationships of arcs and chords in a circle. HOM 10.3 In the same circle, or in congruent circles, two minor arcs are congruent if and only if their
More information14.3 Tangents and Circumscribed Angles
Name lass Date 14.3 Tangents and ircumscribed ngles Essential uestion: What are the key theorems about tangents to a circle? Explore G.5. Investigate patterns to make conjectures about geometric relationships,
More informationWhat You ll Learn. Why It s Important. We see circles in nature and in design. What do you already know about circles?
We see circles in nature and in design. What do you already know about circles? What You ll Learn ircle properties that relate: a tangent to a circle and the radius of the circle a chord in a circle, its
More informationC Given that angle BDC = 78 0 and DCA = Find angles BAC and DBA.
UNERSTNING IRLE THEREMS-PRT NE. ommon terms: (a) R- ny portion of a circumference of a circle. (b) HR- line that crosses a circle from one point to another. If this chord passes through the centre then
More informationMath 9 Chapter 8 Practice Test
Name: Class: Date: ID: A Math 9 Chapter 8 Practice Test Short Answer 1. O is the centre of this circle and point Q is a point of tangency. Determine the value of t. If necessary, give your answer to the
More information10.1 Tangents to Circles. Geometry Mrs. Spitz Spring 2005
10.1 Tangents to Circles Geometry Mrs. Spitz Spring 2005 Objectives/Assignment Identify segments and lines related to circles. Use properties of a tangent to a circle. Assignment: Chapter 10 Definitions
More informationSo, the measure of arc TS is 144. So, the measure of arc QTS is 248. So, the measure of arc LP is Secants, Tangents, and Angle Measures
11-6 Secants, Tangents, Angle Measures Find each measure Assume that segments that appear to be tangent are tangent 4 1 5 So, the measure of arc QTS is 48 So, the measure of arc TS is 144 6 3 So, the measure
More informationMT - MATHEMATICS (71) GEOMETRY - PRELIM II - PAPER - 1 (E)
04 00 eat No. MT - MTHEMTI (7) GEOMETY - PELIM II - PPE - (E) Time : Hours (Pages 3) Max. Marks : 40 Note : (i) ll questions are compulsory. Use of calculator is not allowed. Q.. olve NY FIVE of the following
More information