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
- 7 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 #4-5, assume that the lines that appear to be tangent are tangent. J T For #6-8, 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 12-3 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 - 6-4.) 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.) Re-set 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 40-48**
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 M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships
More informationGeo 9 1 Circles 9-1 Basic Terms associated with Circles and Spheres. Radius. Chord. Secant. Diameter. Tangent. Point of Tangency.
Geo 9 1 ircles 9-1 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 informationChapter Review. 11-1 Lines that Intersect Circles. 11-2 Arcs and Chords. Identify each line or segment that intersects each circle.
HPTR 11-1 hapter Review 11-1 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 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 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 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 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 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 90-degree 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 informationSection 9-1. Basic Terms: Tangents, Arcs and Chords Homework Pages 330-331: 1-18
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 informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical
More informationHow To Understand The Theory Of Ircles
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 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 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 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 informationCK-12 Geometry: Parts of Circles and Tangent Lines
CK-12 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationGEOMETRY COMMON CORE STANDARDS
1st Nine Weeks Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,
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 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 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 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. 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 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 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. 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 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 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 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 informationCSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More informationEUCLIDEAN GEOMETRY: (±50 marks)
ULIN GMTRY: (±50 marks) Grade theorems:. The line drawn from the centre of a circle perpendicular to a chord bisects the chord. 2. The perpendicular bisector of a chord passes through the centre of the
More informationTangent Properties. Line m is a tangent to circle O. Point T is the point of tangency.
CONDENSED LESSON 6.1 Tangent Properties In this lesson you will Review terms associated with circles Discover how a tangent to a circle and the radius to the point of tangency are related Make a conjecture
More informationGeometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More informationAlgebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
More information56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationGeometry - Semester 2. Mrs. Day-Blattner 1/20/2016
Geometry - Semester 2 Mrs. Day-Blattner 1/20/2016 Agenda 1/20/2016 1) 20 Question Quiz - 20 minutes 2) Jan 15 homework - self-corrections 3) Spot check sheet Thales Theorem - add to your response 4) Finding
More informationCurriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.
Curriculum Map by Geometry Mapping for Math Testing 2007-2008 Pre- s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)
More information8.2 Angle Bisectors of Triangles
Name lass Date 8.2 ngle isectors of Triangles Essential uestion: How can you use angle bisectors to find the point that is equidistant from all the sides of a triangle? Explore Investigating Distance from
More informationGeometry. Higher Mathematics Courses 69. Geometry
The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More informationCalculate the circumference of a circle with radius 5 cm. Calculate the area of a circle with diameter 20 cm.
RERTIES F CIRCLE Revision. The terms Diameter, Radius, Circumference, rea of a circle should be revised along with the revision of circumference and area. Some straightforward examples should be gone over
More informationLesson 1.1 Building Blocks of Geometry
Lesson 1.1 Building Blocks of Geometry For Exercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q 2. NQ. 3. nother name for NS is. 4. S is the of SQ. 5. is the midpoint of. 6. NS.
More informationPostulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
More informationGeometry Final Exam Review Worksheet
Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please.
More informationAngle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees
Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in
More informationContents. 2 Lines and Circles 3 2.1 Cartesian Coordinates... 3 2.2 Distance and Midpoint Formulas... 3 2.3 Lines... 3 2.4 Circles...
Contents Lines and Circles 3.1 Cartesian Coordinates.......................... 3. Distance and Midpoint Formulas.................... 3.3 Lines.................................. 3.4 Circles..................................
More informationIMO Training 2008 Circles Yufei Zhao. Circles. Yufei Zhao.
ircles Yufei Zhao yufeiz@mit.edu 1 Warm up problems 1. Let and be two segments, and let lines and meet at X. Let the circumcircles of X and X meet again at O. Prove that triangles O and O are similar.
More informationDraw/Sketch/Interpret a Diagram using Bearings SS6. Calculate the Surface Areas of Prisms, & Cylinders SS7
raw/sketch/interpret a iagram using earings SS6 To save paper this section has been moved to p79 after SS8. alculate the Surface reas of Prisms, & linders SS7 Surface area is the total area of all the
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, January 26, 2016 1:15 to 4:15 p.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, January 26, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The possession or use of any communications
More information2014 2015 Geometry B Exam Review
Semester Eam Review 014 015 Geometr B Eam Review Notes to the student: This review prepares ou for the semester B Geometr Eam. The eam will cover units 3, 4, and 5 of the Geometr curriculum. The eam consists
More informationMATH STUDENT BOOK. 8th Grade Unit 6
MATH STUDENT BOOK 8th Grade Unit 6 Unit 6 Measurement Math 806 Measurement Introduction 3 1. Angle Measures and Circles 5 Classify and Measure Angles 5 Perpendicular and Parallel Lines, Part 1 12 Perpendicular
More informationA summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:
summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment
More informationArea. Area Overview. Define: Area:
Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.
More informationPerpendicular and Parallel Line Segments Worksheet 1 Drawing Perpendicular Line Segments
HPTER10 Perpendicular and Parallel Line Segments Worksheet 1 Drawing Perpendicular Line Segments Fill in the blanks with perpendicular or parallel. D Line is parallel to line D. 1. R P S Line PQ is 2.
More information1-1. Nets and Drawings for Visualizing Geometry. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
1-1 Nets and Drawings for Visualizing Geometry Vocabulary Review Identify each figure as two-dimensional or three-dimensional. 1. 2. 3. three-dimensional two-dimensional three-dimensional Vocabulary uilder
More informationLesson 9.1 The Theorem of Pythagoras
Lesson 9.1 The Theorem of Pythagoras Give all answers rounded to the nearest 0.1 unit. 1. a. p. a 75 cm 14 cm p 6 7 cm 8 cm 1 cm 4 6 4. rea 9 in 5. Find the area. 6. Find the coordinates of h and the radius
More informationThe Geometry of Piles of Salt Thinking Deeply About Simple Things
The Geometry of Piles of Salt Thinking Deeply About Simple Things PCMI SSTP Tuesday, July 15 th, 2008 By Troy Jones Willowcreek Middle School Important Terms (the word line may be replaced by the word
More informationGEOMETRIC MENSURATION
GEOMETRI MENSURTION Question 1 (**) 8 cm 6 cm θ 6 cm O The figure above shows a circular sector O, subtending an angle of θ radians at its centre O. The radius of the sector is 6 cm and the length of the
More informationName: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: ID: A Q3 Geometry Review Multiple Choice Identify the choice that best completes the statement or answers the question. Graph the image of each figure under a translation by the given
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationMath 531, Exam 1 Information.
Math 531, Exam 1 Information. 9/21/11, LC 310, 9:05-9:55. Exam 1 will be based on: Sections 1A - 1F. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/531fa11/531.html)
More informationGeorgia Online Formative Assessment Resource (GOFAR) AG geometry domain
AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent
More informationTeacher Page. 1. Reflect a figure with vertices across the x-axis. Find the coordinates of the new image.
Teacher Page Geometr / Da # 10 oordinate Geometr (5 min.) 9-.G.3.1 9-.G.3.2 9-.G.3.3 9-.G.3. Use rigid motions (compositions of reflections, translations and rotations) to determine whether two geometric
More informationGEOMETRIC FIGURES, AREAS, AND VOLUMES
HPTER GEOMETRI FIGURES, RES, N VOLUMES carpenter is building a deck on the back of a house. s he works, he follows a plan that he made in the form of a drawing or blueprint. His blueprint is a model of
More informationGeometry Made Easy Handbook Common Core Standards Edition
Geometry Made Easy Handbook ommon ore Standards Edition y: Mary nn asey. S. Mathematics, M. S. Education 2015 Topical Review ook ompany, Inc. ll rights reserved. P. O. ox 328 Onsted, MI. 49265-0328 This
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationMATHEMATICS Grade 12 EUCLIDEAN GEOMETRY: CIRCLES 02 JULY 2014
EUCLIDEAN GEOMETRY: CIRCLES 02 JULY 2014 Checklist Make sure you learn proofs of the following theorems: The line drawn from the centre of a circle perpendicular to a chord bisects the chord The angle
More informationSandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.
Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 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 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More informationFinal Review Geometry A Fall Semester
Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over
More informationCONGRUENCE BASED ON TRIANGLES
HTR 174 5 HTR TL O ONTNTS 5-1 Line Segments ssociated with Triangles 5-2 Using ongruent Triangles to rove Line Segments ongruent and ngles ongruent 5-3 Isosceles and quilateral Triangles 5-4 Using Two
More informationMathematics Geometry Unit 1 (SAMPLE)
Review the Geometry sample year-long scope and sequence associated with this unit plan. Mathematics Possible time frame: Unit 1: Introduction to Geometric Concepts, Construction, and Proof 14 days This
More informationD.3. Angles and Degree Measure. Review of Trigonometric Functions
APPENDIX D Precalculus Review D7 SECTION D. Review of Trigonometric Functions Angles and Degree Measure Radian Measure The Trigonometric Functions Evaluating Trigonometric Functions Solving Trigonometric
More informationClassifying Quadrilaterals
1 lassifying Quadrilaterals Identify and sort quadrilaterals. 1. Which of these are parallelograms?,, quadrilateral is a closed shape with 4 straight sides. trapezoid has exactly 1 pair of parallel sides.
More informationEND OF COURSE GEOMETRY
SSSION: 27 P: 1 1/26/04 9:8 OIN IS-joer PT: @sunultra1/raid/s_tpc/rp_va_sprg03/o_03-olptg11/iv_g11geom-1 VIRINI STNRS O RNIN SSSSMNTS Spring 2003 Released Test N O OURS OMTRY Property of the Virginia epartment
More information