Warm Up #23: Review of Circles 1.) A central angle of a circle is an angle with its vertex at the of the circle. Example:


 Bryan Steven Peters
 2 years ago
 Views:
Transcription
1 Geometr hapter 12 Notes Warm Up #23: Review of ircles 1.) central angle of a circle is an angle with its verte at the of the circle. Eample: X 80 2.) n arc is a section of a circle. Eamples:, 3.) We measure arcs in Eample: m 4.) minor arc is a section of a circle that is less than. Eample of a minor arc: 5.) major arc is a section of a circle that is greater than. Eample of a major arc: 6.) The entire arc of a circle measures 7.) semicircle is of a circle (formed b a ) and measures. 8.) Eamples of a semicircle:, E The measure of an arc is equal to the measure of its angle. rc ddition Postulate The sum of the measures of two adjacent arcs is equal to the measurement of the larger arc that the form together. 50 G 80 m m m F 40 Find m<1: 9.) 10.) 11.)
2  2  Notes #23: Tangents (Sections 12.1) Tangents 1.) is a segment, ra, or line that touches a circle onl once. Name four tangents:,, 2.) The point where a tangent touches a circle is called the. X Y Z 3.) Name the point of tangenc: Theorem 12.1 tangent is to the drawn to the point of tangenc. raw this relationship to the left. Use this theorem to complete: K For #45, assume that the lines that appear to be tangent are tangent. J T For #68, JT is tangent to the circle at T 6.) If T = 5, JT = 10, J = 4.) If = 100, find m 7.) If m J 30 and J = 12, JT = 5.) If m 40, find 8.) If JK = 18 and K = 7, then JT =
3  3  Theorem 123 Tangents to a circle from a common point are. Use this corollar to complete: 9.) X = 5, X = X 10.) Find the perimeter of 10 cm F 8cm 15 cm E 11.) Find the perimeter of the quadrilateral: 1.3 in 5.7 in 3.4 in 3.6 in 12.) We sa that a polgon is a circle when all vertices (corners) are on the circle. In this case, we can also sa that the circle is about the polgon. 13.) escribe this figure in two was: 14.) escribe this figure in two was: G P Q F H 15.) raw a circle inscribed in a square. 16.) raw a circle circumscribed about a pentagon.
4  4  ompass Practice: (When using our compass, ou must keep the point (called the center) still.) 17.) Use our compass to make small 18.) Use our compass to make a large circle. circles. Label their centers. Label the center. 19.) Use our compass to draw arcs of a circle. onstruction #1: Given a segment, construct a segment congruent to the given segment (pg. 44) Steps: 1.) Using our straightedge, draw a segment longer than. Pick a point on this segment and label it X. [ur goal is to measure and mark (or cut and paste) onto our new segment.] 2.) Set the width (or radius) of our compass to the length of. This means place the point of our compass on, and then stretch our compass so that the pencil is on point. [You have now stored this length into our compass.] 3.) Without changing the opening of our compass, place its point on X. Use the compass to mark our segment with an arc. Label this intersection as Y. 4.) heck with a ruler that XY onstruct a segment congruent to each given segment: 20.) 21.)
5 Warm Up #24: 1.) Find the perimeter of the quadrilateral: ) is tangent to circle at. If = 12 and m 30, find the length of the radius and the diameter of the circle ) Find the area of a regular heagon with perimeter 96m. 4.) Find the volume of a clinder with diameter 8in and height 10in. Notes #24: Section 12.2 and onstructing ongruent ngles hords (Section 12.2) 1.) and MN are. These segments connect an points on a circle. 2.) What is a name for the longest chord in a circle? 3.) and MN are. These are lines that contain a. M N Theorem 12.4 Y (1) ongruent arcs have congruent. (2) ongruent chords have congruent. X
6  64.) m 5.) m 150 Theorem 12.6 diameter or radius that is to a chord bisects the and its. Use this theorem to complete: (look for right triangles!!) 6.) XY =, iameter = Y M X ) PQ = 16, M =, iameter = 10 Q M P Theorem 12.5 (1) hords that are from the center are (2) chords are from the center **remember that distance is measured with a perpendicular segment, so look for right angles and was to make right triangles** Use this theorem to complete: 8.) M = N = 6, M = 8, EF =, radius =, diameter = E M N F
7  7  onstruction #2: onstruct an angle congruent to the given angle. (pg. 45) Steps: 1.) Using our straightedge, draw a segment. (This will be the base edge of our angle.) Label the left endpoint of the segment E. (This will be the verte of our new angle.) 2.) Set the width (or radius) of our compass to a length shorter than. 3.) Place the center (or point) of our compass at point and draw an arc that passes through both sides of the original angle. Mark these two intersection points as X and Y. 4.) Without changing the width of our compass, draw this same arc with the compass point at E. Mark the intersection point on the base as M. 5.) Reset our compass to the distance between intersection points X and Y. (This measures the width of the original angle.) 6.) Without changing the width of our compass, put the point of our compass on M and draw an arc. Mark this intersection as. 7.) onnect points and E. heck with our protractor that EF onstruct an angle congruent to each given angle: 9.) 10.)
8  8  Warm Up #25: 1.) T = 6, RS = 8, R =, radius =, diameter = S R T 2.) =12, M=8, N=4, EF =, radius =, diameter = M F E N 3.) Solve for : 4 20 Notes #25: Spheres, Inscribed ngles, onstructing Perpendiculars (Section 12.3) plane passes h cm from the center of a sphere with radius R, forming a circle with radius r. Find the indicated values: 1.) R = 5, h = 4, r =? 2.) r = 9, h = 12, R =?
9 n inscribed angle is an angle whose verte is the circle. Eample: 1 2 The measure of an inscribed angle equals the measure of the intercepted arc. Eample: m 1=, m 2 = Special ases: n inscribed angle that intercepts a semicircle is Eample: X The measure of an angle formed b a tangent and a chord equals the measure of its intercepted arc. Eample: Y 120 Z 1 If two inscribed angles intercept the same arc, then the angles are. Eample: 1 2 F G If a quadrilateral is inscribed in a circle, then its opposite angles are E Eample: H Solve for the indicated variables: 3.) =, = 4.) =, = 60 20
10 ) =, = 6.) =, = ) =, =, z = 95 z 8.) =, =, z = z onstructing Perpendicular Lines onstruction #3: Given a point on a line, construct the perpendicular to the line at the given point (pg. 182) 1.) Given point on line k 2.) Using as our center, draw two arcs on line k, one arc to the left of and one to the right of. 3.) Label these new points as X and Y. 4.) Place the center of our compass on X and using a radius larger than X, draw one arc above line k and one arc below line k. 5.) o the same from point Y. oth pairs of arcs must intersect above and below line k. Label these points M and N. 5.) onnect M and N. This segment should intersect point and be perpendicular to line k.
11 onstruct a perpendicular through the indicated point: 9.) 10.) onstruction #4: Given a point outside a line, construct the perpendicular to the line from the given point (pg. 183) Steps: 1.) Place the center of our compass on point P. 2.) Using a consistent width, draw two arcs that intersect line k. Label these points X and Y. 3.) From X, draw an arc below line k 4.) From Y, draw an arc below line k 5.) These two arcs must intersect. Label this intersection Z. 6.) onnect P and Z; this segment is perpendicular to line k. onstruct the perpendicular segment from P through line k. 11.) 12.) P P k k
12 Warm Up #26: Quiz Review 1.) Find the perimeter of the quadrilateral ) is tangent to circle at. If = 18 and m 30, find the length of the radius and the diameter of the circle ) Name one of each: a) central angle b) chord c) secant d) inscribed angle X Y 4.) T = 12, ST = 16, R =, radius =, diameter = T S R 5.) z w = = = w 80 z =
13 Warm Up #27: Solve for the variables ) 2.) z ) 50 z v 20 w 4.) =12, M=3, N= 2 5, EF =, radius =, diameter = M E N F Notes #27: ngle Measures and Segment Lengths (Section 12.4), Review of onstructions Interior and Eterior ngles Theorem (Part I) a b n angle formed b two chords is equal to the of its two intercepted arcs. (interior angle) = (arc + arc) 2 Solve for : 1.) 2.) 3.)
14 Theorem (Part II) n eterior angle formed b (a) two secants, (b) two tangents, or (c) one tangent and one secant is equal to the of its two intercepted arcs. (eterior angle) = (arc  arc) 2 (a) (b) (c) a b a b a b Solve for and : 4.) 5.) ) 7.)
15 omplete the constructions: 8.) onstruct a segment congruent to the given segment: 9.) onstruct an angle congruent to the given angle: M L 10.) onstruct a line perpendicular to the given line through the given point: 11.) onstruct a line perpendicular to the given line through the given point: 12.) onstruct a line perpendicular to the given line through the given point: 13.) onstruct a line perpendicular to the given line through the given point: 14.) onstruct an angle congruent to the given angle:
16 Warm Up #28: ircle Review 1.) Find M and MQ 2.) Find M and MQ P M Q P M Q 3.) Find and 4.) Find and Notes #28: Segment Lengths, onstructing Parallel Lines and Perpendicular isectors (Section 12.4) Segment Lengths in ircles Theorem (Part I) a b When two chords intersect in a circle, the product of the of one chord equals the product of the of the other chord (piece)(piece) = (piece)(piece) Solve for : 1.) 2.)
17 Theorem (Part II) When (a) two secants or (b) one tangent and one secant are drawn to a circle, then: (a) (eterior segment)(whole length) = (eterior segment)(whole length) (b) a b a b Solve for the variables: 3.) 4.) ) 6.) ) 6 8.) )
18 onstruction #5: Given a point outside a line, construct the parallel to the given line through the given point (pg. 181) Steps: 1.) raw points and, in that order and not too far apart, on line k. 2.) raw P and etend this ra a considerable distance. (t P, we will construct an angle congruent and corresponding to P.) 3.) Set our compass to the width of. With the center of our compass at, draw an arc that passes through line k and P. Mark the new point of intersection as X. 4.) Without changing the width of our compass, put its center at P and draw a similar arc above and to the right of point P. Mark the intersect as M. point where this arc and P 5.) hange the width of our compass to be the length X. 6.) Keeping this width, put the center of our compass on M and draw an arc that intersects the previous arc. Mark this point of intersection as N. 7.) raw PN. This line is parallel to line k. onstruct the parallel line to k through P. 10.) 11.) P P k k onstruction #6: onstruct a perpendicular bisector to a given segment (pg. 46) Steps: 1.) Set the width (or radius) of our compass to a length longer than half the given segment. 2.) With the center of our compass on point, draw one arc above and one arc below the segment. 3.) With the center of our compass on point, draw one arc above and one arc below the segment. 4.) Make sure that ou find where these pairs of arcs intersect. Mark these points as X and Y. 5.) onnect X and Y; this is our perpendicular bisector.
19 ) 13.) Warm Up #29: ircle Review Solve for the variables: 1.) 2.) ) 4.) Notes #29: ircles in the oordinate Plane, onstructing ngle isectors (Section 12.5) ircles Equations of circles are written in this form: ( h) ( k) r Where (h, k) is the of the circle and r is the of the circle Graph and find the equation of each circle: Graph the center point From this point, go the distance of the radius up, down, left, and right onnect these 4 points as a circle
20 1.) (2, 4) r = 4 2.) (5, 0), r = 3 Name the center and radius of each circle, then graph ) 4.) 2 2 ( 1) ( 2) 9 ( 4) Write the standard equation of each circle: Find the center point From this point, count the distance to the highest point on the circle. This is the radius. 5.) 6.)
21 Write the standard equation of the circle with the given center that passes through the given point: Plug the center point into the standard equation as (h, k) Plug the second point into that equation as (, ) Solve for r. Plug into equation from first step. 7.) circle has a center (1, 3) and passes through the point (4, 1). Find the equation of this circle and graph it. 8.) Find the equation of the circle whose center is (3, 2) and goes through the point (1, 2). onstruction #7: onstruct the bisector of a given angle (pg. 47) Steps: 1.) Set the width (or radius) of our compass to a length shorter than. 2.) Place the center (or point) of our compass at point and draw an arc that passes through both sides of the original angle. Mark these two intersection points as X and Y. 3.) Keeping the same width, place the center of our compass at point X and draw an arc in the interior of the angle. o the eact same process with our compass at point Y. 4.) Label the intersections of these two interior arcs Z 5.) Using our straightedge, draw Z 6.) Z bisects Using onl a compass and a straightedge, bisect the given angles: 9.) 10.)
22 HW #30 Geometr hapter 12 Stud Guide Name : Necessar Skills: Pthagorean Theorem and Special Right Triangles. Solve for and 1.) 2.) 3.) 4.) Ke Vocabular: Name one eample of each 5.) a. radius b. diameter E c. chord d. secant e. tangent f. point of tangenc g. central angle i. minor arc h. inscribed angle j. major arc 6.) raw each: b. circle circumscribed about an obtuse triangle. a. rectangle inscribed in a circle Tangents: 7.) omplete: JT is tangent to the circle at T a.) If T = 4, J = 12, then JT = b.) If m J 30 and JT= 12, J =, T = c.) If JK = 4 and K = 6, then JT = K J T entral and Inscribed ngles: Solve for and 8.) 9.) ) ) ) ) F G 110 E H
23 ) ) ) hords and rcs: 17.) ) T = 12, RS = 4, R =, radius =, diameter= S R T 19.) = 6, M = 4, N = 3, EF =, radius =, diam. = M F E N 20.) EF = 8, N = 3, M = 2, = M F E N Interior and Eterior ngles: Solve for 21.) 22.) 23.) ) 25.) 26.) Segments and Lengths: Solve for 27.) 28.) 29.)
24 ) 31.) 6 32.) Find the perimeter of each polgon: 33.) 34.) 7 cm 13 cm 1.9 in 3.7 in 3.4 in 5 cm 6 cm 3.6 in omplete the problems about circles: 35.) Find the equation of the circle with center at (2, 7) and radius ) Find the equation of the circle whose center is (3, 1) and goes through the point (1, 2) 37.) Find the center and the radius of the circle described b: (  5) 2 + ( +3) 2 = 9. Graph ) chord is 4m from the center of a circle. If the radius of the circle is 10m, how long is the chord? 38.) Find the equation of the circle shown here: 40.) sphere is sliced b a plane 2ft from the center of the sphere. If the radius of the circular plane made b the plane s slice is 8ft, what is the radius of the sphere? **on t forget worksheet problems 4048**
Circle Name: Radius: Diameter: Chord: Secant:
12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane
More informationCCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name:
GPS UNIT 3 Semester 1 NLYTI GEOMETRY Page 1 of 3 ircles and Volumes Name: ate: Understand and apply theorems about circles M91.G..1 Prove that all circles are similar. M91.G.. Identify and describe relationships
More informationGeo 9 1 Circles 91 Basic Terms associated with Circles and Spheres. Radius. Chord. Secant. Diameter. Tangent. Point of Tangency.
Geo 9 1 ircles 91 asic Terms associated with ircles and Spheres ircle Given Point = Given distance = Radius hord Secant iameter Tangent Point of Tangenc Sphere Label ccordingl: ongruent circles or spheres
More informationGeometry SOL G.11 G.12 Circles Study Guide
Geometry SOL G.11 G.1 Circles Study Guide Name Date Block Circles Review and Study Guide Things to Know Use your notes, homework, checkpoint, and other materials as well as flashcards at quizlet.com (http://quizlet.com/4776937/chapter10circlesflashcardsflashcards/).
More informationChapters 6 and 7 Notes: Circles, Locus and Concurrence
Chapters 6 and 7 Notes: Circles, Locus and Concurrence IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of
More informationChapter Review. 111 Lines that Intersect Circles. 112 Arcs and Chords. Identify each line or segment that intersects each circle.
HPTR 111 hapter Review 111 Lines that Intersect ircles Identify each line or segment that intersects each circle. 1. m 2. N L K J n W Y X Z V 3. The summit of Mt. McKinley in laska is about 20,321 feet
More informationChapter 6 Notes: Circles
Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment
More informationGEOMETRY FINAL EXAM REVIEW
GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.
More informationGeometry Unit 10 Notes Circles. Syllabus Objective: 10.1  The student will differentiate among the terms relating to a circle.
Geometry Unit 0 Notes ircles Syllabus Objective: 0.  The student will differentiate among the terms relating to a circle. ircle the set of all points in a plane that are equidistant from a given point,
More informationIntro to Circles Formulas Area: Circumference: Circle:
Intro to ircles Formulas rea: ircumference: ircle: Key oncepts ll radii are congruent If radii or diameter of 2 circles are congruent, then circles are congruent. Points with respect to ircle Interior
More informationTangents to Circles. Circle The set of all points in a plane that are equidistant from a given point, called the center of the circle
10.1 Tangents to ircles Goals p Identify segments and lines related to circles. p Use properties of a tangent to a circle. VOULRY ircle The set of all points in a plane that are equidistant from a given
More informationFor the circle above, EOB is a central angle. So is DOE. arc. The (degree) measure of ù DE is the measure of DOE.
efinition: circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. We use the symbol to represent a circle. The a line segment from the center
More informationcircumscribed circle Vocabulary Flash Cards Chapter 10 (p. 539) Chapter 10 (p. 530) Chapter 10 (p. 538) Chapter 10 (p. 530)
Vocabulary Flash ards adjacent arcs center of a circle hapter 10 (p. 539) hapter 10 (p. 530) central angle of a circle chord of a circle hapter 10 (p. 538) hapter 10 (p. 530) circle circumscribed angle
More informationCoordinate Graphing and Geometric Constructions
HPTER 9 oordinate Graphing and Geometric onstructions hapter Vocabular coordinate plane origin graph image line of reflection rotation midpoint ais ordered pair quadrants translation line smmetr rotational
More informationGeometry Chapter 10 Study Guide Name
eometry hapter 10 Study uide Name Terms and Vocabulary: ill in the blank and illustrate. 1. circle is defined as the set of all points in a plane that are equidistant from a fixed point called the center.
More informationACT Math Vocabulary. Altitude The height of a triangle that makes a 90degree angle with the base of the triangle. Altitude
ACT Math Vocabular Acute When referring to an angle acute means less than 90 degrees. When referring to a triangle, acute means that all angles are less than 90 degrees. For eample: Altitude The height
More informationThe measure of an arc is the measure of the central angle that intercepts it Therefore, the intercepted arc measures
8.1 Name (print first and last) Per Date: 3/24 due 3/25 8.1 Circles: Arcs and Central Angles Geometry Regents 20132014 Ms. Lomac SLO: I can use definitions & theorems about points, lines, and planes to
More informationBC AB = AB. The first proportion is derived from similarity of the triangles BDA and ADC. These triangles are similar because
150 hapter 3. SIMILRITY 397. onstruct a triangle, given the ratio of its altitude to the base, the angle at the vertex, and the median drawn to one of its lateral sides 398. Into a given disk segment,
More informationLesson 1: Introducing Circles
IRLES N VOLUME Lesson 1: Introducing ircles ommon ore Georgia Performance Standards M9 12.G..1 M9 12.G..2 Essential Questions 1. Why are all circles similar? 2. What are the relationships among inscribed
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationSection 91. Basic Terms: Tangents, Arcs and Chords Homework Pages 330331: 118
Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,
More informationcircle the set of all points that are given distance from a given point in a given plane
Geometry Week 19 Sec 9.1 to 9.3 Definitions: section 9.1 circle the set of all points that are given distance from a given point in a given plane E D Notation: F center the given point in the plane radius
More informationSenior Math Circles: Geometry I
Universit of Waterloo Facult of Mathematics entre for Education in Mathematics and omputing pening Problem (a) If 30 7 = + + z Senior Math ircles: Geometr I, where, and z are positive integers, then what
More informationDuplicating Segments and Angles
ONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson you will Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using
More informationGeometry Chapter 9. Circle Vocabulary Arc Length Angle & Segment Theorems with Circles Proofs
Geometry hapter 9 ircle Vocabulary rc Length ngle & Segment Theorems with ircles Proofs hapter 9: ircles Date Due Section Topics ssignment 9.1 9.2 Written Eercises Definitions Worksheet (pg330 classroom
More informationc.) If RN = 2, find RP. N
Geometry 101 ircles and ircumference. Parts of ircles 1. circle is the locus of all points equidistant from a given point called the center of the circle.. circle is usually named by its point. 3. The
More informationGeometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: Activity 24
Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: ctivity 24 esources: Springoard Geometry Unit Overview In this unit, students will study formal definitions of basic figures,
More informationFor each Circle C, find the value of x. Assume that segments that appear to be tangent are tangent. 1. x = 2. x =
Name: ate: Period: Homework  Tangents For each ircle, find the value of. ssume that segments that appear to be tangent are tangent. 1. =. = ( 5) 1 30 0 0 3. =. = (Leave as simplified radical!) 3 8 In
More informationA geometric construction is a drawing of geometric shapes using a compass and a straightedge.
Geometric Construction Notes A geometric construction is a drawing of geometric shapes using a compass and a straightedge. When performing a geometric construction, only a compass (with a pencil) and a
More informationSec 1.1 CC Geometry  Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB.
Sec 1.1 CC Geometry  Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have
More informationA = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height
Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side
More informationCK12 Geometry: Parts of Circles and Tangent Lines
CK12 Geometry: Parts of Circles and Tangent Lines Learning Objectives Define circle, center, radius, diameter, chord, tangent, and secant of a circle. Explore the properties of tangent lines and circles.
More informationName Geometry Exam Review #1: Constructions and Vocab
Name Geometry Exam Review #1: Constructions and Vocab Copy an angle: 1. Place your compass on A, make any arc. Label the intersections of the arc and the sides of the angle B and C. 2. Compass on A, make
More informationDefinitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
More informationChapter 4 Circles, TangentChord Theorem, Intersecting Chord Theorem and Tangentsecant Theorem
Tampines Junior ollege H3 Mathematics (9810) Plane Geometry hapter 4 ircles, Tangenthord Theorem, Intersecting hord Theorem and Tangentsecant Theorem utline asic definitions and facts on circles The
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More information121. Tangent Lines. Vocabulary. Review. Vocabulary Builder HSM11_GEMC_1201_T Use Your Vocabulary
11 Tangent Lines Vocabulary Review 1. ross out the word that does NT apply to a circle. arc circumference diameter equilateral radius. ircle the word for a segment with one endpoint at the center of a
More informationCircle Theorems. This circle shown is described an OT. As always, when we introduce a new topic we have to define the things we wish to talk about.
Circle s circle is a set of points in a plane that are a given distance from a given point, called the center. The center is often used to name the circle. T This circle shown is described an OT. s always,
More information2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
More informationChapter 1 Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1.
Name: lass: ate: I: hapter 1 Exam Multiple hoice Identify the choice that best completes the statement or answers the question. 1. bisects, m = (7x 1), and m = (4x + 8). Find m. a. m = c. m = 40 b. m =
More information10.1: Areas of Parallelograms and Triangles
10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a
More information6.2 PLANNING. Chord Properties. Investigation 1 Defining Angles in a Circle
LESSN 6.2 You will do foolish things, but do them with enthusiasm. SINIE GRIELL LETTE Step 1 central Step 1 angle has its verte at the center of the circle. Step 2 n Step 2 inscribed angle has its verte
More informationFinal Review Problems Geometry AC Name
Final Review Problems Geometry Name SI GEOMETRY N TRINGLES 1. The measure of the angles of a triangle are x, 2x+6 and 3x6. Find the measure of the angles. State the theorem(s) that support your equation.
More information0810ge. Geometry Regents Exam 0810
0810ge 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More informationLesson 3.1 Duplicating Segments and Angles
Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each
More informationRelevant Vocabulary. The MIDPOINT of a segment is a point that divides a segment into 2 = or parts.
im 9: How do we construct a perpendicular bisector? Do Now: 1. omplete: n angle bisector is a ray (line/segment) that divides an into two or parts. 48 Geometry 10R 2. onstruct and label D, the bi sector
More informationDuplicating Segments and Angles
CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty
More informationName Date Class. Lines and Segments That Intersect Circles. AB and CD are chords. Tangent Circles. Theorem Hypothesis Conclusion
Section. Lines That Intersect Circles Lines and Segments That Intersect Circles A chord is a segment whose endpoints lie on a circle. A secant is a line that intersects a circle at two points. A tangent
More informationConstruct a Segment Bisector: Using a Compass
onstruct a Segment isector: Using a ompass 1. raw a segment and label it. 2. Use a compass to draw a circle using point as the centre. Make sure the circle cuts the segment more than halfway to point.
More informationGEOMETRY OF THE CIRCLE
HTR GMTRY F TH IRL arly geometers in many parts of the world knew that, for all circles, the ratio of the circumference of a circle to its diameter was a constant. Today, we write d 5p, but early geometers
More informationOverview Mathematical Practices Congruence
Overview Mathematical Practices Congruence 1. Make sense of problems and persevere in Experiment with transformations in the plane. solving them. Understand congruence in terms of rigid motions. 2. Reason
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationGeometry Vocabulary. Created by Dani Krejci referencing:
Geometry Vocabulary Created by Dani Krejci referencing: http://mrsdell.org/geometry/vocabulary.html point An exact location in space, usually represented by a dot. A This is point A. line A straight path
More informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More informationUnit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find
More informationGeometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam.
Geometry Review Here are some formulas and concepts that you will need to review before working on the practice eam. Triangles o Perimeter or the distance around the triangle is found by adding all of
More informationGEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
More informationCentroid: The point of intersection of the three medians of a triangle. Centroid
Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:
More information10.5 and 10.6 Lesson Plan
Title: Secants, Tangents, and Angle Measures 10.5 and 10.6 Lesson Plan Course: Objectives: Reporting Categories: Related SOL: Vocabulary: Materials: Time Required: Geometry (Mainly 9 th and 10 th Grade)
More informationThe Inscribed Angle Alternate A Tangent Angle
Student Outcomes Students use the inscribed angle theorem to prove other theorems in its family (different angle and arc configurations and an arc intercepted by an angle at least one of whose rays is
More informationGEOMETRY. Constructions OBJECTIVE #: G.CO.12
GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
More informationUnit 3 Circles and Spheres
Accelerated Mathematics I Frameworks Student Edition Unit 3 Circles and Spheres 2 nd Edition March, 2011 Table of Contents INTRODUCTION:... 3 Sunrise on the First Day of a New Year Learning Task... 8 Is
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More informationTrade of Metal Fabrication. Module 5: Pipe Fabrication Unit 9: Segmental Bends Phase 2
Trade of Metal Fabrication Module 5: Pipe Fabrication Unit 9: Segmental Bends Phase 2 Table of Contents List of Figures... 5 List of Tables... 5 Document Release History... 6 Module 5 Pipe Fabrication...
More information1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
More informationTest to see if ΔFEG is a right triangle.
1. Copy the figure shown, and draw the common tangents. If no common tangent exists, state no common tangent. Every tangent drawn to the small circle will intersect the larger circle in two points. Every
More information3. Lengths and areas associated with the circle including such questions as: (i) What happens to the circumference if the radius length is doubled?
1.06 Circle Connections Plan The first two pages of this document show a suggested sequence of teaching to emphasise the connections between synthetic geometry, coordinate geometry (which connects algebra
More informationLesson 6.1 Tangent Properties
Lesson 6.1 angent roperties Name eriod ate 1. Ras r and s are tangents. w 2. is tangent to both circles and m 295. mqx r w 54 s 3. Q is tangent to two eternall tangent noncongruent circles, and N. X Q
More informationGEOMETRY COMMON CORE STANDARDS
1st Nine Weeks Experiment with transformations in the plane GCO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,
More informationChapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.
Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.
More informationCircle geometry theorems
Circle geometry theorems http://topdrawer.aamt.edu.au/geometricreasoning/bigideas/circlegeometry/angleandchordproperties Theorem Suggested abbreviation Diagram 1. When two circles intersect, the line
More informationDates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday. 3 (only see 6 th, 4
Name: Period GL UNIT 12: IRLS I can define, identify and illustrate the following terms: Interior of a circle hord xterior of a circle Secant of a circle Tangent to a circle Point of tangency entral angle
More informationINDEX. Arc Addition Postulate,
# 3060 right triangle, 441442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More information1. Construct a large circle and label its centre C. D Construct a chord AB and a central angle BCA. Measure BCA.
10.1 ploring ngles in a ircle Focus on fter this lesson, ou will be able to describe a relationship between inscribed angles in a circle relate the inscribed angle and central angle subtended b the same
More informationD.2. The Cartesian Plane. The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles. D10 APPENDIX D Precalculus Review
D0 APPENDIX D Precalculus Review APPENDIX D. The Cartesian Plane The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles The Cartesian Plane Just as ou can represent real numbers b
More informationCIRCLE DEFINITIONS AND THEOREMS
DEFINITIONS Circle The set of points in a plane equidistant from a given point(the center of the circle). Radius A segment from the center of the circle to a point on the circle(the distance from the
More informationCONJECTURES  Discovering Geometry. Chapter 2
CONJECTURES  Discovering Geometry Chapter C1 Linear Pair Conjecture  If two angles form a linear pair, then the measures of the angles add up to 180. C Vertical Angles Conjecture  If two angles are
More informationBasics of Circles 9/20/15. Important theorems:
Basics of ircles 9/20/15 B H P E F G ID Important theorems: 1. A radius is perpendicular to a tangent at the point of tangency. PB B 2. The measure of a central angle is equal to the measure of its intercepted
More informationof one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
2901 Clint Moore Road #319, Boca Raton, FL 33496 Office: (561) 4592058 Mobile: (949) 5108153 Email: HappyFunMathTutor@gmail.com www.happyfunmathtutor.com GEOMETRY THEORUMS AND POSTULATES GEOMETRY POSTULATES:
More informationNCERT. In examples 1 and 2, write the correct answer from the given four options.
MTHEMTIS UNIT 2 GEOMETRY () Main oncepts and Results line segment corresponds to the shortest distance between two points. The line segment joining points and is denoted as or as. ray with initial point
More informationGeometry Enduring Understandings Students will understand 1. that all circles are similar.
High School  Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,
More informationNew York State Student Learning Objective: Regents Geometry
New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students
More information*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.
Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review
More informationGrade 7 & 8 Math Circles Circles, Circles, Circles March 19/20, 2013
Faculty of Mathematics Waterloo, Ontario N2L 3G Introduction Grade 7 & 8 Math Circles Circles, Circles, Circles March 9/20, 203 The circle is a very important shape. In fact of all shapes, the circle is
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your
More informationSkills Practice Workbook
Workbook ontents Include: 96 worksheets one for each lesson To The Student: This Workbook gives ou additional problems for the concept eercises in each lesson. The eercises are designed to aid our stud
More informationGeometry Chapter 1 Vocabulary. coordinate  The real number that corresponds to a point on a line.
Chapter 1 Vocabulary coordinate  The real number that corresponds to a point on a line. point  Has no dimension. It is usually represented by a small dot. bisect  To divide into two congruent parts.
More informationGeometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles
Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.
More informationYears t. Definition Anyone who has drawn a circle using a compass will not be surprised by the following definition of the circle: x 2 y 2 r 2 304
Section The Circle 65 Dollars Purchase price P Book value = f(t) Salvage value S Useful life L Years t FIGURE 3 Straightline depreciation. The Circle Definition Anone who has drawn a circle using a compass
More informationD.2. The Cartesian Plane. The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles. D10 APPENDIX D Precalculus Review
D0 APPENDIX D Precalculus Review SECTION D. The Cartesian Plane The Cartesian Plane The Distance and Midpoint Formulas Equations of Circles The Cartesian Plane An ordered pair, of real numbers has as its
More informationGeometry Unit 5: Circles Part 1 Chords, Secants, and Tangents
Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents Name Chords and Circles: A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.
More informationAn inscribed polygon is a polygon whose vertices are points of a circle. in means in and scribed means written
Geometry Week 6 Sec 3.5 to 4.1 Definitions: section 3.5 A A B D B D C Connect the points in consecutive order with segments. C The square is inscribed in the circle. An inscribed polygon is a polygon whose
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationUnit 3: Circles and Volume
Unit 3: 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 informationSet 1: Circumference, Angles, Arcs, Chords, and Inscribed Angles
Goal: To provide opportunities for students to develop concepts and skills related to circumference, arc length, central angles, chords, and inscribed angles Common Core Standards Congruence Experiment
More information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
More information