MODULE. (40 + 8x) + (5x -16) = 180. STUDY GUIDE REVIEW Angles and Segments in Circles. Key Vocabulary
|
|
- Rosaline Eaton
- 5 years ago
- Views:
Transcription
1 STUDY GUIDE REVIEW Angles and Segments in ircles ODULE 15 Essential Question: How can you use angles and segments in circles to solve real-world problems? EY EXALE (Lesson 15.1) Determine m DE, m BD, m DAB, and m ADE. Since chord AE passes through the center of the circle at, the chord AE is a diameter of the circle. ABE is then a semicircle, and m ABE = 180. But m ADE = 1 2 m ABE = 90. ΔADE is a right triangle with m AED = 36. (40 +8x) J A 54 L B 18 Also, m DAE = 1 2 m DE, which implies that m DE = 2m DAE = 108. Since m BD = m BE + m DE, m BD = = 126. Finally, m DAB = 1 2 m BD = 63. EY EXALE (Lesson 15.2) Determine the angles J,, L, and in the given quadrilateral. (40 + 8x) + (5x -16) = x = x = 156. x = 12. m J = x = (12) = 136 m L = 5x - 16 = 5 (12) - 16 = = (12) m = _ = 60. m + m = m = = 120 D (5x 16) E 20x 4 ey Vocabulary chord (cuerda) central angle (ángulo central) inscribed angle (ángulo inscrito) arc (arco) minor arc (arco menor) major arc (arco principal) semicircle (semicirculo) adjacent arcs (arcos adyacentes) Inscribed Angle Theorem (teorema del ángulo inscrito) Inscribed Quadrilateral Theorem (teorema del ángulo inscrito) tangent (tangent) point of tangency (punto de tangencia) Tangent-Radius Theorem (teorema de la tangenteradio) hord-hord roduct Theorem (teorema del producto de la cuerda de la cuerda) secant (secante) secant segment (segmente secante) external secant segment (segmento externo secante) Secant-Secant Theorem (Teorema de la secantesecante) tangent segment (segmento tangente) Intersecting hords Angle easure Theorem (teorema de medida de ángulo de intersección acordes) Tangent-Secant Interior Angle easure Theorem (teorema de la medida de ángulo interior tangente-secante) Tangent-Secant Exterior Angle easure Theorem (teorema de la medida de ángulo exterior tangente-secante) odule Study Guide Review
2 EY EXALE (Lesson 15.3) Two tangent lines are drawn to a circle from point intersecting the circle at points and N. If m N = 210, what is m N? N If m N = 210, then m N = = 150. m N = 1_ 2 (m N - m N ) m N = 1_ ( ) = 1_ (60 ) = EY EXALE (Lesson 15.4) A tangent and a secant are drawn to a circle from the external point B. The point of tangency is at point A, and the secant intersects the circle at points and D. Find x. From the Secant-Tangent roduct Theorem, we can say that BD B = AB 2. So (2 + x) 2 = 8 2. A B 8 2 x D So 4 + 2x = 64. 2x = 60 and x = 30. EY EXALE (Lesson 15.5) Two chords intersect the interior of a circle at point T. Find m R. By the Intersecting hords Angle easure Theorem we can say the following: m QTS = 1_ 2 (m QS + m R ) 60 = 1_ 2 (80 + m R ) 120 = (80 + m R ) = m R 40 = m R R T 60 Q 80 S odule Study Guide Review
3 EXERISES Use the Inscribed Angle Theorem. (Lesson 15.1) 1. Find the measure of the intercepted arc for an inscribed angle of 50. Use the Inscribed Quadrilateral Theorem. (Lesson 15.2) 2. If one angle of a quadrilateral inscribed in a circle is 50, what is the measure of its opposite angle? Use the ircumscribed Angle Theorem. (Lesson 15.3) 3. Two tangents are drawn from an external point A to a circle. If one of the intercepted arcs on the circle is 120, what must be the measure of the other intercepted arc? Use the hord-hord roduct Theorem. (Lesson 15.4) R T S Q Given RT = 2, TS = 6, and T = 3. Find TQ Use the Tangent-Secant Exterior Angle easure Theorem. (Lesson 15.5) L Find m L in the diagram given the m and m JN. J N 83 odule Study Guide Review
4 ODULE ERFORANE TAS How any arbles Will Fit? onsider a package of marbles in the shape of a triangular prism. The cross-section of the package is an equilateral triangle with a side length of 1.5 inches, and the length of the package is 10 inches. What is the diameter of the largest marble that will fit inside the package? How many such marbles can fit within the package? Start by listing in the space below how you plan to tackle the problem. Then use your own paper to complete the task. Be sure to write down all your data and assumptions. Then use words, numbers, diagrams, or algebra to explain how you reached your conclusion. odule Study Guide Review
5 Ready to Go On? Angles and Segments in ircles 1. If m BD = 20 and m EF = 34, determine m ABD using the appropriate theorems and postulates. (Lesson 15.1) If m EF = 34, then m EF =. If m EF = 34, then m AB = by the Theorem. If m AB = 34 and m BD = 20, then Online Homework Hints and Help Extra ractice A m AB = and. By the so m ABD =., m ABD = m AB + m BD, and 2. Find the measures of each angle in the inscribed quadrilateral. (Lesson 15.2) E F D B (y ) Q (5y + 4) R (15y + 16) S Fill in the proper conclusions based on known theorems and relationships. (Lesson 15.5) 3. Using the given figure where _ and _ N are tangent to the circle at and N respectively, what can you say about the following? a. What angles are right angles? b. Suppose that m N = 80. What is m N? ESSENTIAL QUESTION 4. What are the major theorems that allow you to determine the relationships between angles formed by lines that intersect a circle? N odule Study Guide Review
6 ODULE 15 IXED REVIEW Assessment Readiness SELETED RESONSE 1. An angle of 20 is inscribed in a circle. ould the given value be the measure of the arc intercepted by this angle? Select Yes or No for A. A. 10 Yes No B. 20 Yes No. 40 Yes No 2. The points A, B,, and D are taken in order on the circumference of a circle. hords A and BD intersect at point E. m AB = 76 and m D = 80. hoose True or False for each statement. A. m AB = 156 True False B. m AEB = 78 True False. m AED = 72 True False 3. Line BF bisects AB, m ABF = 6x, and m FB = (2x + 60). hoose True or False for each statement. A. m FB = 45 True False B. m AB = 180 True False. ABF is a right angle. True False 4. If two chords intersect inside a circle, then what do you know about the products of the lengths of the segments of the chords? How can you determine whether two circles are similar? 5. AB is inscribed in a circle such that vertices A and B lie on a diameter of the circle. If the length of the diameter of the circle is 13 and the length of chord B is 5, find side A. odule Study Guide Review
Study 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 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 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 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 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 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 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 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 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 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 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 informationChapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in
Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.
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 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 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 informationHonors 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 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 informationCircles and Volume. Circle Theorems. Essential Questions. Module Minute. Key Words. What To Expect. Analytical Geometry Circles and Volume
Analytical Geometry Circles and Volume Circles and Volume There is something so special about a circle. It is a very efficient shape. There is no beginning, no end. Every point on the edge is the same
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 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 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 informationPlane geometry Circles: Problems with some Solutions
The University of Western ustralia SHL F MTHMTIS & STTISTIS UW MY FR YUNG MTHMTIINS Plane geometry ircles: Problems with some Solutions 1. Prove that for any triangle, the perpendicular bisectors of the
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 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 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 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 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 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 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 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 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 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 informationWest Haven Public Schools Unit Planning Organizer
West Haven Public Schools Unit Planning Organizer Subject: Circles and Other Conic Sections Grade 10 Unit: Five Pacing: 4 weeks + 1 week Essential Question(s): 1. What is the relationship between angles
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 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 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 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 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 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 informationSo, the measure of arc TS is Secants, Tangents, and Angle Measures
Find each measure. Assume that segments that appear to be tangent are tangent. 1. 3. 110 73 2. 4. So, the measure of arc TS is 144. 144 31 esolutions Manual - Powered by Cognero Page 1 5. 7. STUNTS A ramp
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 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 informationKEY EXAMPLE (Lesson 23.1) Find the coordinates of the circumcenter of the triangle. Coordinates: A (-2, -2), B (2, 3), C (2, -2) 2) Midpoint of BC
Houghton Mifflin Harcourt Publishing ompan STUDY GUIDE REVIEW Special Segments in Triangles Essential Question: How can ou use special segments in triangles to solve real-world problems? KEY EXMPLE (Lesson
More information) = (0, -2) Midpoint of AC ) = ( 2, MODULE. STUDY GUIDE REVIEW Special Segments in Triangles
Houghton Mifflin Harcourt Publishing ompan STUDY GUIDE REVIEW Special Segments in Triangles Essential Question: How can ou use special segments in triangles to solve real-world problems? KEY EXMPLE (Lesson
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 informationUNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction
Prerequisite Skills This lesson requires the use of the following skills: performing operations with fractions understanding slope, both algebraically and graphically understanding the relationship of
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 information15.5 Angle Relationships in Circles
ame lass ate 15.5 ngle Relationships in ircles ssential uestion: What are the relationships between angles formed by lines that intersect a circle? xplore xploring ngle Measures in ircles The sundial is
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 informationMath 3 Quarter 4 Overview
Math 3 Quarter 4 Overview EO5 Rational Functions 13% EO6 Circles & Circular Functions 25% EO7 Inverse Functions 25% EO8 Normal Distribution 12% Q4 Final 10% EO5 Opp #1 Fri, Mar 24th Thu, Mar 23rd ML EO5
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 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 informationMid-Chapter Quiz: Lessons 10-1 through Refer to. 1. Name the circle. SOLUTION: The center of the circle is A. Therefore, the circle is ANSWER:
Refer to. 1. Name the circle. The center of the circle is A. Therefore, the circle is 2. Name a diameter. ; since is a chord that passes through the center, it is a diameter. 3. Name a chord that is not
More information1 What is the solution of the system of equations graphed below? y = 2x + 1
1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x
More informationKEY STANDARDS ADDRESSED: MM2G3. Students will understand the properties of circles.
KEY STANDARDS ADDRESSED:. Students will understand the properties of circles. a. Understand and use properties of chords, tangents, and secants an application of triangle similarity. b. Understand and
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 informationUnderstand and Apply Theorems about Circles
UNIT 4: CIRCLES AND VOLUME This unit investigates the properties of circles and addresses finding the volume of solids. Properties of circles are used to solve problems involving arcs, angles, sectors,
More informationEvaluate: Homework and Practice
valuate: Homework and ractice Use the figure for ercises 1 2. Suppose ou use geometr software to construct two chords S and TU that intersect inside a circle at V. Online Homework Hints and Help tra ractice
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 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 informationAlgebra II/Geometry Curriculum Guide Dunmore School District Dunmore, PA
Algebra II/Geometry Dunmore School District Dunmore, PA Algebra II/Geometry Prerequisite: Successful completion of Algebra 1 Part 2 K Algebra II/Geometry is intended for students who have successfully
More information10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2)
10. Circles Q 1 True or False: It is possible to draw two circles passing through three given non-collinear points. Mark (1) Q 2 State the following statement as true or false. Give reasons also.the perpendicular
More information0612ge. Geometry Regents Exam
0612ge 1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent
More informationWARM UP. Sunday, November 16, 2014
WARM UP Sunday, November 16, 2014 1 2 3 4 5 6 7 8 9 10 Objectives Use properties of circles to derive the formula for sector area. Determine arc length and arc measure for given central and inscribed angle
More informationHomework Problems Set 24
Homework Problems Set 24 Proof 6.3.1 (1) ACB & ADB both intercept arc Assumption for Conditional Proof AB in O (2) m ACB = ½ m(arc AB) By (1), Theorem 6.9 (3) m ADB = ½ m(arc AB) By (1), Theorem 6.9 (4)
More information0811ge. Geometry Regents Exam
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationTopic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths
Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is
More informationPRACTICE TEST 1 Math Level IC
SOLID VOLUME OTHER REFERENCE DATA Right circular cone L = cl V = volume L = lateral area r = radius c = circumference of base h = height l = slant height Sphere S = 4 r 2 V = volume r = radius S = surface
More information0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
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 informationCircles. Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: Angles & Arcs Class Work
Circles Parts of a Circle Class Work Use the diagram of the circle with center A to answer the following: 1. Name the radii 2. Name the chord(s) 3. Name the diameter(s) 4. If AC= 7, what does TC=? 5. If
More informationLesson 2B: Thales Theorem
Lesson 2B: Thales Theorem Learning Targets o I can identify radius, diameter, chords, central circles, inscribed circles and semicircles o I can explain that an ABC is a right triangle, then A, B, and
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 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 information16 circles. what goes around...
16 circles. what goes around... 2 lesson 16 this is the first of two lessons dealing with circles. this lesson gives some basic definitions and some elementary theorems, the most important of which is
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 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 informationright angle an angle whose measure is exactly 90ᴼ
right angle an angle whose measure is exactly 90ᴼ m B = 90ᴼ B two angles that share a common ray A D C B Vertical Angles A D C B E two angles that are opposite of each other and share a common vertex two
More information21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.
21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then
More information1) With a protractor (or using CABRI), carefully measure nacb and write down your result.
4.5 The Circle Theorem Moment for Discovery: Inscribed Angles Draw a large circle and any of its chords AB, as shown. Locate three points C, C', and C'' at random on the circle and on the same side of
More informationBOARD QUESTION PAPER : MARCH 2016 GEOMETRY
BOARD QUESTION PAPER : MARCH 016 GEOMETRY Time : Hours Total Marks : 40 Note: (i) Solve All questions. Draw diagram wherever necessary. (ii) Use of calculator is not allowed. (iii) Diagram is essential
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 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 informationLesson 7.1: Central Angles
Lesson 7.1: Central Angles Definition 5.1 Arc An arc is a part of a circle. Types of Arc 1. Minor Arc 2. Major Arc 3. Semicircle Figure 5.1 Definition 5.2 Central Angle A central angle of a circle is an
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 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 information10. Show that the conclusion of the. 11. Prove the above Theorem. [Th 6.4.7, p 148] 4. Prove the above Theorem. [Th 6.5.3, p152]
foot of the altitude of ABM from M and let A M 1 B. Prove that then MA > MB if and only if M 1 A > M 1 B. 8. If M is the midpoint of BC then AM is called a median of ABC. Consider ABC such that AB < AC.
More information0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
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 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 information(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2
CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5
More informationArkansas Council of Teachers of Mathematics 2012 State Competition Geometry Exam. B. 28 (5x-41) 3 m (2x+25)
rkansas ouncil of Teachers of Mathematics 2012 State ompetition Geometry Exam For questions 1 through 25, mark your answer choice on the answer sheet provided. (Figures may not be drawn to scale.) fter
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 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 informationThe Coordinate Plane. Circles and Polygons on the Coordinate Plane. LESSON 13.1 Skills Practice. Problem Set
LESSON.1 Skills Practice Name Date The Coordinate Plane Circles and Polgons on the Coordinate Plane Problem Set Use the given information to show that each statement is true. Justif our answers b using
More informationLiberal High School Lesson Plans
Monday, 5/8/2017 Liberal High School Lesson Plans er:david A. Hoffman Class:Algebra III 5/8/2017 To 5/12/2017 Students will perform math operationsto solve rational expressions and find the domain. How
More informationTangents and Circles, Part 1
Tangents and Circles, Part 1 A tangent line lies in the same plane as a circle and intersects the circle at exactly one point. A radius of a circle drawn to a point of tangency meets the tangent line at
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 informationLabel carefully each of the following:
Label carefully each of the following: Circle Geometry labelling activity radius arc diameter centre chord sector major segment tangent circumference minor segment Board of Studies 1 These are the terms
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 information