Unit 9 Syllabus: Circles


 Egbert McDowell
 2 years ago
 Views:
Transcription
1 ate Period Unit 9 Syllabus: ircles ay Topic 1 Tangent Lines 2 hords and rcs and Inscribed ngles 3 Review/Graded lasswork 4 Review from before reak 5 Finding ngle Measures 6 Finding Segment Lengths 7 Review 8 Test
2 ate Period Tangent Lines  Unit 9 ay 1 1. tangent line is a line that intersects a circle in exactly. The word tangent may refer to a,, or. 2. line that intersects a circle in two points is called a line. a. More on this to come 3. Today s goal: emonstrate an understanding of two important properties of tangents. If a line is drawn tangent to a circle, and a radius is drawn to the point of tangency then the tangent line and radius are. * The converse is also true! Important Property #1 If two lines are tangent to the same circle then the segments from their intersection to the point of tangency are. Important Property #2
3 4. Wonderful applications of the two important properties a. Tangent segments and radii create 5 y 3 5 x 12 3 b. ircumscribed polygons Triangle is about the circle ircle is in the triangle Quadrilateral is in the circle ircle is about the quadrilateral Find the Perimeter! 8.
4 5. pulley system (proof p. 664) 12 x Smaller radius = 10 Larger radius = 24 What is the distance from center to center? a. 48 b. losure: escribe the two properties of tangents that we learned today!
5 ate Period hords, rcs, and Inscribed ngles  Unit 9 ay 2 Important properties that hold within one circle, or in two (or more) congruent circles Z Y X x In Summary a) ongruent central angles have congruent chords b) ongruent chords have congruent arcs c) ongruent arcs have congruent central angles d) hords equidistant from the center are congruent/bisected by the radius
6 Two chords create an angle. The arc that is formed is called an arc. 1. The Inscribed ngle Theorem: The measure of the inscribed angle is the measure of its intercepted arc a) Rightngle orollary: If an inscribed angle intercepts a semicircle, then the angle is right Y XTZ is a semicircle So XTZ = 180º T O XYZ intercepts XTZ, so it is half the measure Therefore half of 180º is 90º Z b) rcintercept orollary: If two inscribed angles intercept the same arc, then they have the same measure. intercepts so it is half the measure, 1 Thus = 60 = º intercepts so it is half the measure, 1 Thus = 60 = 30 2 ecause both angles have to be half of 60º  that means that they must both be equal. Thus, m = m because they both equal 30º. c) The opposite angles of a quadrilateral inscribed in a circle are.
7 ) 8) 9) 10) 11) 12)
8 In circle P shown below, m 1 = 50 and mf = 75. Find each angle and arc below P 5 3 F E m 2 = m 9 = m 3 = m 10 = m 4 = m 11 = m 5 = m = m 6 = m = m 7 = m = m 8 = me = mef =
9 ate Period Unit 9 ay 4: Post Holiday reak Review!
10
11 ate Period Finding ngle Measures  Unit 9 ay 5 1. The measure of an angle formed by two secants or chords that intersect in the interior of a circle is the of the measures of the arcs intercepted by the angle and its vertical angle. Intersects INSIE the circle. Note: F is NOT the center X F 40º Y ngles are congruent because they are vertical angles XFW = 110 because it is supplementary W 100º Z 1 WFZ = 70 2 ( ) = INSIE the circle is + 2. The measure of an angle formed in the exterior of a circle is the of the measures of the intercepted arcs. 1 MG = ( ) = 50 Intersection OUTSIE the circle 2 110º 10º OUTSIE the circle is  G E M F X R 260º Y 60º Z 20º 15 S 100º T
12 Summary of ngles Vertex is on the circle Vertex is inside the circle Vertex is outside the circle X Y W X F Y Z G F E M 1 X = 2 ( ) 1 Y = 2 ( ) 1 WFZ = + 2 ( WZ XY ) 1 WFX = + 2 ( WX YZ) 1 MG = 2 ( G EF ) In the space below, compare and contrast the three properties shown above, as well as the central angle theorem (how does the measure of a central angle compare to the measure of its arc)? raw pictures if you want irections: Find each missing variable below 1) 2) 3)
13 In circle P shown below, T is tangent, E and are diameters, plus me = 50, m = 80, and m = mg. 4 E P T G m 1 = m 2 = m 9 = m 3 = m 10 = m 4 = m 11 = m 5 = m 12 = m 6 = m 13 = m 7 = m 14 = m 8 = m 15 =
14 + ate Period Segment Lengths  Unit 9 ay 6 1. We can find the lengths of pieces of chords, secants and tangents a. Identifying the different parts of secant and tangent lines. tangent line X is a tangent segment secant line is a chord X X is a secant segment referred to as the Whole X is an external secant segment referred to as the Outside b. Two Tangent Segments Theorem i. If two segments are tangent to a circle at the same external point, then the segments are congruent (we saw this on day 1 already!) because they are both tangent segments oth tangents intersect at the same point
15 c. Two Secants Theorem i. If two secants intersect outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment 18 8 X X and X are both secant segments (Whole) X and X are both external segments (Outside) 16 9 Two secants intersect outside the circle Whole X Outside = Whole X Outside X X = X X 18 8 = 16 9 = 144 d. Secant and Tangent Theorem i. If a secant and a tangent intersect outside a circle, then the product of the lengths of the secant segment and its external segment equals the length of the tangent segment squared. EX is a tangent segment X is a secant segment (Whole) GX is an external secant segment (Outside) E 6 G 4 X Whole X Outside = Tangent Squared X GX = EX = 6 = e. Two hords Theorem i. If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the product of the lengths of the segment of the other chord. X is not the center! 3 4 X 8 6 X X = X X 4 6 = 3 8 = 24
16
17 Wrap Up  Summary of Segment Lengths irections: Write formulas, in terms of the letters given, that illustrate the 3 formulas a c d b x w y z t z y
18 ate Period Unit 9 Review Unit 9 ay 7 1) 2) Find m Given: is tangent to circle O at, mef = 214, m = 144. Find me 3) 4) Find m 5) 6)
19 7) 8) 9) 10) 100º me m m E m 140º P 40º E PE PE EP E 11) 12) P is the center. Prove: P P O = 5 = 2 3 O =? ( rounded) P
20 ate Period You must get at least 10 angles correct to receive any points
Unit 10 Circles 101 Properties of Circles Circle  the set of all points equidistant from the center of a circle. Chord  A line segment with
Unit 10 Circles 101 Properties of Circles Circle  the set of all points equidistant from the center of a circle. Chord  A line segment with endpoints on the circle. Diameter  A chord which passes through
More informationGeometry Definitions and Theorems. Chapter 9. Definitions and Important Terms & Facts
Geometry Definitions and Theorems Chapter 9 Definitions and Important Terms & Facts A circle is the set of points in a plane at a given distance from a given point in that plane. The given point is the
More information6.1 Circles and Related Segments and Angles
Chapter 6 Circles 6.1 Circles and Related Segments and Angles Definitions 32. A circle is the set of all points in a plane that are a fixed distance from a given point known as the center of the circle.
More informationExamples: The name of the circle is: The radii of the circle are: The chords of the circle are: The diameter of the circle is:
Geometry P Lesson 101: ircles and ircumference Page 1 of 1 Objectives: To identify and use parts of circles To solve problems involving the circumference of a circle Geometry Standard: 8 Examples: The
More informationChapter 6. Sir Migo Mendoza
Circles Chapter 6 Sir Migo Mendoza Central Angles Lesson 6.1 Sir Migo Mendoza Central Angles Definition 5.1 Arc An arc is a part of a circle. Types of Arc Minor Arc Major Arc Semicircle Definition 5.2
More informationTopic 7: Properties of Circles
This Packet Belongs to (Student Name) Topic 7: Properties of Circles Unit 6 Properties of Circles Module 15: Angles and Segments in Circles 15.1 Central Angles and Inscribed Angles 15.2 Angles in Inscribed
More information101 Circles & Circumference
101 Circles & Circumference Radius Circle Formula Chord Diameter Circumference Formula Formula Two circles are congruent if and only if they have congruent radii All circles are similar Concentric
More informationNOTES: Tangents to Circles
Unit# ssign # TS: Tangents to ircles GL Identify segments and lines related to circles and use properties of a tangent to a circle VULRY circle is the set of all points in a plane that are equidistant
More informationHonors Geometry Chapter 6 Tentative Syllabus
Honors Geometry hapter 6 Tentative Syllabus YOU R XPT TO HK YOUR NSWRS FOR OMING TO LSS. Red ay Red ate lue ay lue ate Topic Homework (due next class period) Fri Nov 20 Mon Nov 23 6.1 Tangent Properties
More informationGeometry: A Complete Course
Geometry: omplete ourse with Trigonometry) Module Progress Tests Written by: Larry. ollins Geometry: omplete ourse with Trigonometry) Module  Progress Tests opyright 2014 by VideotextInteractive Send
More informationCircles  Probability
Section 101: Circles and Circumference SOL: G.10 The student will investigate and solve practical problems involving circles, using properties of angles, arcs, chords, tangents, and secants. Problems
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES GEOMETRY. 3 rd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES GEOMETRY 3 rd Nine Weeks, 20162017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource for
More informationHonors Geometry CHAPTER 7. Study Guide Final Exam: Ch Name: Hour: Try to fill in as many as possible without looking at your book or notes.
Honors Geometry Study Guide Final Exam: h 7 12 Name: Hour: Try to fill in as many as possible without looking at your book or notes HPTER 7 1 Pythagorean Theorem: Pythagorean Triple: 2 n cute Triangle
More informationMATH 30 GEOMETRY UNIT OUTLINE AND DEFINITIONS Prepared by: Mr. F.
1 MTH 30 GEMETRY UNIT UTLINE ND DEFINITINS Prepared by: Mr. F. Some f The Typical Geometric Properties We Will Investigate: The converse holds in many cases too! The Measure f The entral ngle Tangent To
More informationCircles and Polygons LongTerm Memory Review Review 1 (Note: Figures are not drawn to scale.)
Review 1 (Note: Figures are not drawn to scale.) 1. Fill in the lank: In circle below, the angle shown is a/an angle. 2. The measure of a central angle and the measure of the arc that it intersects are
More informationSTANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY 3 rd Nine Weeks, 20162017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
More informationVideos, Constructions, Definitions, Postulates, Theorems, and Properties
Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos Proof Overview: http://tinyurl.com/riehlproof Modules 9 and 10: http://tinyurl.com/riehlproof2 Module 9 Review: http://tinyurl.com/module9livelessonrecording
More informationTheorems & Postulates Math Fundamentals Reference Sheet Page 1
Math Fundamentals Reference Sheet Page 1 3060 90 Triangle In a 3060 90 triangle, the length of the hypotenuse is two times the length of the shorter leg, and the length of the longer leg is the length
More informationName Date. Inscribed Angles and Polygons For use with Exploration arcs? How are the angles of an inscribed quadrilateral related to each other?
Name ate 10.4 Inscribed ngles and Polygons For use with Exploration 10.4 Essential Question How are inscribed angles related to their intercepted arcs? How are the angles of an inscribed quadrilateral
More informationThe Bronx High School of Science, Mathematics Department. Trigonometry (M$6) Mr. J. Fox, Instructor M$6 CIRCLE REVIEW SHEET
The ronx High School of Science, Mathematics epartment Valerie Reidy, rincipal Rosemarie Jahoda,.. Mathematics Trigonometry (M$6) Mr. J. Fox, Instructor M$6 IRLE REVIEW SHEET Note: This review sheet was
More informationNotes Circle Basics Standard:
Notes Circle Basics M RECALL EXAMPLES Give an example of each of the following: 1. Name the circle 2. Radius 3. Chord 4. Diameter 5. Secant 6. Tangent (line) 7. Point of tangency 8. Tangent (segment) DEFINTION
More informationadded to equal quantities, their sum is equal. Same holds for congruence.
Mr. Cheung s Geometry Cheat Sheet Theorem List Version 6.0 Updated 3/14/14 (The following is to be used as a guideline. The rest you need to look up on your own, but hopefully this will help. The original
More informationb. find the lateral area of the cylinder c. If the radius is doubled, what happens to the volume?
im: How do we find the volume and surface area of pyramids? o Now: If the radius and the height of a cylinder is 4 a. find the volume of the cylinder b. find the lateral area of the cylinder c. If the
More informationGeometry: A Complete Course
Geometry: omplete ourse with Trigonometry) Module Instructor's Guide with etailed Solutions for Progress Tests Written by: Larry. ollins RRT /010 Unit V, Part, Lessons 1, uiz Form ontinued. Match each
More informationModeling with Geometry
Modeling with Geometry 6.3 Parallelograms https://mathbitsnotebook.com/geometry/quadrilaterals/qdparallelograms.html Properties of Parallelograms Sides A parallelogram is a quadrilateral with both pairs
More informationTheta Circles & Polygons 2015 Answer Key 11. C 2. E 13. D 4. B 15. B 6. C 17. A 18. A 9. D 10. D 12. C 14. A 16. D
Theta Circles & Polygons 2015 Answer Key 1. C 2. E 3. D 4. B 5. B 6. C 7. A 8. A 9. D 10. D 11. C 12. C 13. D 14. A 15. B 16. D 17. A 18. A 19. A 20. B 21. B 22. C 23. A 24. C 25. C 26. A 27. C 28. A 29.
More informationPerimeter. Area. Surface Area. Volume. Circle (circumference) C = 2πr. Square. Rectangle. Triangle. Rectangle/Parallelogram A = bh
Perimeter Circle (circumference) C = 2πr Square P = 4s Rectangle P = 2b + 2h Area Circle A = πr Triangle A = bh Rectangle/Parallelogram A = bh Rhombus/Kite A = d d Trapezoid A = b + b h A area a apothem
More informationGeometry: A Complete Course
Geometry: omplete ourse with Trigonometry) Module E Solutions Manual Written by: Larry E. ollins Geometry: omplete ourse with Trigonometry) Module E Solutions Manual opyright 2014 by VideotextInteractive
More informationCHAPTER 7. Circles. Copyright Big Ideas Learning, LLC All rights reserved.
HPTER 7 ircles 7.1 Lines and Segments that Intersect ircles...45 7. Finding rc Measures...51 7.3 Using hords...57 7.4 Inscribed ngles and Polygons...63 7.5 ngle Relationships in ircles...69 7.6 Segment
More informationLines That Intersect Circles
LESSON 111 Lines That Intersect Circles Lesson Objectives (p. 746): Vocabulary 1. Interior of a circle (p. 746): 2. Exterior of a circle (p. 746): 3. Chord (p. 746): 4. Secant (p. 746): 5. Tangent of
More informationGeometry Rules. Triangles:
Triangles: Geometry Rules 1. Types of Triangles: By Sides: Scalene  no congruent sides Isosceles  2 congruent sides Equilateral  3 congruent sides By Angles: Acute  all acute angles Right  one right
More informationPostulates, Theorems, and Corollaries. Chapter 1
Chapter 1 Post. 111 Through any two points there is exactly one line. Post. 112 Through any three noncollinear points there is exactly one plane containing them. Post. 113 If two points lie in a
More informationPlane Geometry. Paul Yiu. Department of Mathematics Florida Atlantic University. Summer 2011
lane Geometry aul Yiu epartment of Mathematics Florida tlantic University Summer 2011 NTENTS 101 Theorem 1 If a straight line stands on another straight line, the sum of the adjacent angles so formed is
More informationHigh School Geometry. Correlation of the ALEKS course High School Geometry to the ACT College Readiness Standards for Mathematics
High School Geometry Correlation of the ALEKS course High School Geometry to the ACT College Readiness Standards for Mathematics Standard 5 : Graphical Representations = ALEKS course topic that addresses
More informationSOME IMPORTANT PROPERTIES/CONCEPTS OF GEOMETRY (Compiled by Ronnie Bansal)
1 SOME IMPORTANT PROPERTIES/CONCEPTS OF GEOMETRY (Compiled by Ronnie Bansal) 1. Basic Terms and Definitions: a) Linesegment: A part of a line with two end points is called a linesegment. b) Ray: A part
More informationGeometry: A Complete Course (with Trigonometry)
Geometry: omplete ourse with Trigonometry) Module  Student WorkTet Written by: Thomas. lark Larry. ollins Geometry: omplete ourse with Trigonometry) Module Student Worktet opyright 014 by VideotetInteractive
More informationHave students complete the summary table, and then share as a class to make sure students understand concepts.
Closing (5 minutes) Have students complete the summary table, and then share as a class to make sure students understand concepts. Lesson Summary: We have just developed proofs for an entire family of
More informationAcknowledgement: Scott, Foresman. Geometry. SIMILAR TRIANGLES. 1. Definition: A ratio represents the comparison of two quantities.
1 cknowledgement: Scott, Foresman. Geometry. SIMILR TRINGLS 1. efinition: ratio represents the comparison of two quantities. In figure, ratio of blue squares to white squares is 3 : 5 2. efinition: proportion
More informationName Class Date. Lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x?
121 Practice Tangent Lines Lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. To start, identify the type of geometric figure formed by the tangent
More informationCarnegie Learning High School Math Series: Geometry Indiana Standards Worktext Correlations
Carnegie Learning High School Math Series: Logic and Proofs G.LP.1 Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates,
More informationGeometry: Traditional Pathway
GEOMETRY: CONGRUENCE G.CO Prove geometric theorems. Focus on validity of underlying reasoning while using variety of ways of writing proofs. G.CO.11 Prove theorems about parallelograms. Theorems include:
More informationWork with a partner. Use dynamic geometry software.
10.4 Inscribed ngles and Polygons ssential uestion How are inscribed angles related to their intercepted arcs? How are the angles of an inscribed quadrilateral related to each other? n inscribed angle
More informationMANHATTAN HUNTER SCIENCE HIGH SCHOOL GEOMETRY CURRICULUM
COORDINATE Geometry Plotting points on the coordinate plane. Using the Distance Formula: Investigate, and apply the Pythagorean Theorem as it relates to the distance formula. (G.GPE.7, 8.G.B.7, 8.G.B.8)
More informationChapter 10 Similarity
Chapter 10 Similarity Def: The ratio of the number a to the number b is the number. A proportion is an equality between ratios. a, b, c, and d are called the first, second, third, and fourth terms. The
More informationProperties of a Circle Diagram Source:
Properties of a Circle Diagram Source: http://www.ricksmath.com/circles.html Definitions: Circumference (c): The perimeter of a circle is called its circumference Diameter (d): Any straight line drawn
More information2 nd Semester Final Exam Review
2 nd Semester Final xam Review I. Vocabulary hapter 7 cross products proportion scale factor dilation ratio similar extremes scale similar polygons indirect measurements scale drawing similarity ratio
More informationMath 7, Unit 08: Geometric Figures Notes
Math 7, Unit 08: Geometric Figures Notes Points, Lines and Planes; Line Segments and Rays s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My
More informationPearson Mathematics Geometry
A Correlation of Pearson Mathematics Geometry Indiana 2017 To the INDIANA ACADEMIC STANDARDS Mathematics (2014) Geometry The following shows where all of the standards that are part of the Indiana Mathematics
More informationGEOMETRY is the study of points in space
CHAPTER 5 Logic and Geometry SECTION 51 Elements of Geometry GEOMETRY is the study of points in space POINT indicates a specific location and is represented by a dot and a letter R S T LINE is a set of
More informationGeometry Practice. 1. Angles located next to one another sharing a common side are called angles.
Geometry Practice Name 1. Angles located next to one another sharing a common side are called angles. 2. Planes that meet to form right angles are called planes. 3. Lines that cross are called lines. 4.
More informationHigh School Mathematics Geometry Vocabulary Word Wall Cards
High School Mathematics Geometry Vocabulary Word Wall Cards Table of Contents Reasoning, Lines, and Transformations Basics of Geometry 1 Basics of Geometry 2 Geometry Notation Logic Notation Set Notation
More informationReteaching Inequalities in Two Triangles
Name ate lass Inequalities in Two Triangles INV You have worked with segments and angles in triangles. Now ou will eplore inequalities with triangles. Hinge Theorem If two sides of one triangle are congruent
More informationArkansas Council of Teachers of Mathematics State Contest. Geometry Exam
rkansas ouncil of Teachers of Mathematics 2013 State ontest Geometry Exam In each of the following choose the EST answer and shade the corresponding letter on the Scantron Sheet. nswer all 25 multiple
More informationIndex COPYRIGHTED MATERIAL. Symbols & Numerics
Symbols & Numerics. (dot) character, point representation, 37 symbol, perpendicular lines, 54 // (double forward slash) symbol, parallel lines, 54, 60 : (colon) character, ratio of quantity representation
More informationFRANKLINSIMPSON HIGH SCHOOL
FRANKLINSIMPSON HIGH SCHOOL Course Name: Geometry Unit Name: Going in Circles Quality Core Objectives: B.1. C.1. D.1. Mathematical Processes Logic and Proof Points, Lines, Planes, and Space Unit 13 Going
More informationInstructional Unit CPM Geometry Unit Content Objective Performance Indicator Performance Task State Standards Code:
306 Instructional Unit Area 1. Areas of Squares and The students will be Find the amount of carpet 2.4.11 E Rectangles able to determine the needed to cover various plane 2. Areas of Parallelograms and
More informationTriangle Geometry Isometric Triangles Lesson 1
Triangle eometry Isometric Triangles Lesson 1 Review of all the TORMS in OMTRY that you know or soon will know!. Triangles 1. The sum of the measures of the interior angles of a triangle is 180º (Triangle
More informationGeometry A YearataGlance YearataGlance
YearataGlance 20182019 YearataGlance FIRST SEMESTER SECOND SEMESTER Unit 1 Foundations of Geometry Unit 2 Circles Unit 3 Equations of Lines and AnglePairs Unit 4 Congruence Unit 5 Triangles 1st
More informationYEAR AT A GLANCE Student Learning Outcomes by Marking Period
20142015 Term 1 Overarching/general themes: Tools to Build and Analyze Points, Lines and Angles Dates Textual References To Demonstrate Proficiency by the End of the Term Students Will : Marking Period
More information107 Special Segments in a Circle. Find x. Assume that segments that appear to be tangent are tangent. 1. SOLUTION: 2. SOLUTION: 3.
Find x. Assume that segments that appear to be tangent are tangent. 1. 2. 3. esolutions Manual  Powered by Cognero Page 1 4. 5. SCIENCE A piece of broken pottery found at an archaeological site is shown.
More informationAngles. An angle is: the union of two rays having a common vertex.
Angles An angle is: the union of two rays having a common vertex. Angles can be measured in both degrees and radians. A circle of 360 in radian measure is equal to 2π radians. If you draw a circle with
More informationStandards to Topics. Common Core State Standards 2010 Geometry
Standards to Topics GCO.01 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance
More information0613ge. Geometry Regents Exam 0613
wwwjmaporg 0613ge 1 In trapezoid RSTV with bases and, diagonals and intersect at Q If trapezoid RSTV is not isosceles, which triangle is equal in area to? 2 In the diagram below, 3 In a park, two straight
More informationUNIT 5 GEOMETRY TEMPLATE CREATED BY REGION 1 ESA UNIT 5
UNIT 5 GEOMETRY TEMPLATE CREATED BY REGION 1 ESA UNIT 5 Geometry Unit 5 Overview: Circles With and Without Coordinates In this unit, students prove basic theorems about circles, with particular attention
More informationIndicate whether the statement is true or false.
Math 121 Fall 2017  Practice Exam  Chapters 5 & 6 Indicate whether the statement is true or false. 1. The simplified form of the ratio 6 inches to 1 foot is 6:1. 2. The triple (20,21,29) is a Pythagorean
More informationPASS. 5.2.b Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry.
Geometry Name Oklahoma cademic tandards for Oklahoma P PRCC odel Content Frameworks Current ajor Curriculum Topics G.CO.01 Experiment with transformations in the plane. Know precise definitions of angle,
More informationMath 7, Unit 8: Geometric Figures Notes
Math 7, Unit 8: Geometric Figures Notes Points, Lines and Planes; Line Segments and Rays s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My guess
More informationGeometry Final Exam  Study Guide
Geometry Final Exam  Study Guide 1. Solve for x. True or False? (questions 25) 2. All rectangles are rhombuses. 3. If a quadrilateral is a kite, then it is a parallelogram. 4. If two parallel lines are
More informationa B. 3a D. 0 E. NOTA m RVS a. DB is parallel to EC and AB=3, DB=5, and
Geometry Individual Test NO LULTOR!!! Middleton Invitational February 18, 006 The abbreviation "NOT" denotes "None of These nswers." iagrams are not necessarily drawn to scale. 1. Which set does not always
More information11.4 CIRCUMFERENCE AND ARC LENGTH 11.5 AREA OF A CIRCLE & SECTORS
11.4 CIRCUMFERENCE AND ARC LENGTH 11.5 AREA OF A CIRCLE & SECTORS Section 4.1, Figure 4.2, Standard Position of an Angle, pg. 248 Measuring Angles The measure of an angle is determined by the amount of
More information3. Radius of incenter, C. 4. The centroid is the point that corresponds to the center of gravity in a triangle. B
1. triangle that contains one side that has the same length as the diameter of its circumscribing circle must be a right triangle, which cannot be acute, obtuse, or equilateral. 2. 3. Radius of incenter,
More informationUnit Number of Days Dates. 1 Angles, Lines and Shapes 14 8/2 8/ Reasoning and Proof with Lines and Angles 14 8/22 9/9
8 th Grade Geometry Curriculum Map Overview 20162017 Unit Number of Days Dates 1 Angles, Lines and Shapes 14 8/2 8/19 2  Reasoning and Proof with Lines and Angles 14 8/22 9/9 3  Congruence Transformations
More informationGeometry Vocabulary Math Fundamentals Reference Sheet Page 1
Math Fundamentals Reference Sheet Page 1 Acute Angle An angle whose measure is between 0 and 90 Acute Triangle A that has all acute Adjacent Alternate Interior Angle Two coplanar with a common vertex and
More informationCommon Core Specifications for Geometry
1 Common Core Specifications for Geometry Examples of how to read the red references: Congruence (GCo) 203 indicates this spec is implemented in Unit 3, Lesson 2. IDT_C indicates that this spec is implemented
More information2) Draw a labeled example of : a) a ray b) a line c) a segment. 5) Which triangle congruency conjecture would be used for each of the following?
eometry Semester Final Review Name Period ) raw an example of four collinear points. 2) raw a labeled example of : a) a ray b) a line c) a segment 3) Name this angle four ways: 4) raw a concave polygon
More informationHoughton Mifflin Harcourt Geometry 2015 correlated to the New York Common Core Learning Standards for Mathematics Geometry
Houghton Mifflin Harcourt Geometry 2015 correlated to the New York Common Core Learning Standards for Mathematics Geometry Standards for Mathematical Practice SMP.1 Make sense of problems and persevere
More informationCURRICULUM GUIDE. Honors Geometry
CURRICULUM GUIDE Honors Geometry This level of Geometry is approached at an accelerated pace. Topics of postulates, theorems and proofs are discussed both traditionally and with a discovery approach. The
More informationAngles. Classification Acute Right Obtuse. Complementary s 2 s whose sum is 90 Supplementary s 2 s whose sum is 180. Angle Addition Postulate
ngles Classification cute Right Obtuse Complementary s 2 s whose sum is 90 Supplementary s 2 s whose sum is 180 ngle ddition Postulate If the exterior sides of two adj s lie in a line, they are supplementary
More informationTable of Contents. Unit 3: Circles and Volume. Answer Key...AK1. Introduction... v
These materials may not be reproduced for any purpose. The reproduction of any part for an entire school or school system is strictly prohibited. No part of this publication may be transmitted, stored,
More informationMadison County Schools Suggested Geometry Pacing Guide,
Madison County Schools Suggested Geometry Pacing Guide, 2016 2017 Domain Abbreviation Congruence GCO Similarity, Right Triangles, and Trigonometry GSRT Modeling with Geometry *GMG Geometric Measurement
More informationWest WindsorPlainsboro Regional School District Basic Geometry Grades 912
West WindsorPlainsboro Regional School District Basic Geometry Grades 912 Unit 1: Basics of Geometry Content Area: Mathematics Course & Grade Level: Basic Geometry, 9 12 Summary and Rationale This unit
More informationGREE CASTLE A TRIM HIGH SCHOOL PLA ED COURSE Board Approved: March 2010
GREE CASTLE A TRIM HIGH SCHOOL PLA ED COURSE Board Approved: March 2010 COURSE TITLE: GEOMETRY GRADE LEVEL (S): 9, 10, 11 COURSE TEXT: GEOMETRY, HOLT/RINEHART/WINSTON, 1991 EDITION LIST OF TOPICS: REVIEW
More informationLines Plane A flat surface that has no thickness and extends forever.
Lines Plane A flat surface that has no thickness and extends forever. Point an exact location Line a straight path that has no thickness and extends forever in opposite directions Ray Part of a line that
More informationBasic Euclidean Geometry
hapter 1 asic Euclidean Geometry This chapter is not intended to be a complete survey of basic Euclidean Geometry, but rather a review for those who have previously taken a geometry course For a definitive
More informationNEW YORK GEOMETRY TABLE OF CONTENTS
NEW YORK GEOMETRY TABLE OF CONTENTS CHAPTER 1 POINTS, LINES, & PLANES {G.G.21, G.G.27} TOPIC A: Concepts Relating to Points, Lines, and Planes PART 1: Basic Concepts and Definitions...1 PART 2: Concepts
More informationTerm Definition Figure
Notes LT 1.1  Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruency, parallel, perpendicular, etc.) Term Definition Figure collinear on the same line (note: you do
More informationEUCLID S GEOMETRY. Raymond Hoobler. January 27, 2008
EUCLID S GEOMETRY Raymond Hoobler January 27, 2008 Euclid rst codi ed the procedures and results of geometry, and he did such a good job that even today it is hard to improve on his presentation. He lived
More informationThe scale factor between the blue diamond and the green diamond is, so the ratio of their areas is.
For each pair of similar figures, find the area of the green figure. 1. The scale factor between the blue diamond and the green diamond is, so the ratio of their areas is. The area of the green diamond
More information11.5 Inscribed Angles and
age 1 of 6 11.5 Inscribed ngles and olygons Goal Use properties of inscribed angles. ey Words inscribed angle intercepted arc inscribed circumscribed n inscribed angle is an angle whose vertex is on a
More informationGeometry: Concept Categories Concept Category 1 (CC1): Transformations & Basic Definitions
Concept Category 1 (CC1): Transformations & Basic Definitions Concept Category 2 (CC2): Triangles (Similarity and Properties) Concept Category 3 (CC3): Triangle Trigonometry Concept Category 4 (CC4): Triangle
More informationMath 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK
Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK [acute angle] [acute triangle] [adjacent interior angle] [alternate exterior angles] [alternate interior angles] [altitude] [angle] [angle_addition_postulate]
More informationPreliminary: First you must understand the relationship between inscribed and circumscribed, for example:
10.7 Inscribed and Circumscribed Polygons Lesson Objective: After studying this section, you will be able to: Recognize inscribed and circumscribed polygons Apply the relationship between opposite angles
More informationGeometry First Semester Practice Final (cont)
49. Determine the width of the river, AE, if A. 6.6 yards. 10 yards C. 12.8 yards D. 15 yards Geometry First Semester Practice Final (cont) 50. In the similar triangles shown below, what is the value of
More informationGEOMETRY PRECISION GLEs
GEOMETRY PRECISION GLEs NUMBER AND NUMBER RELATIONS GLE.1 GLE.2 GLE.3 Simplify and determine the value of radical expressions Predict the effect of operations on real numbers (e.g., the quotient of a positive
More information1. AREAS. Geometry 199. A. Rectangle = base altitude = bh. B. Parallelogram = base altitude = bh. C. Rhombus = 1 product of the diagonals = 1 dd
Geometry 199 1. AREAS A. Rectangle = base altitude = bh Area = 40 B. Parallelogram = base altitude = bh Area = 40 Notice that the altitude is different from the side. It is always shorter than the second
More informationGeometric Terminology
Geometric Terminology Across 3. An angle measuring 180. 5. Non coplanar, non intersecting lines. 6. Two angles that add to 90. 8. In a right triangle, one of the shorter sides. 9. Lines that form right
More informationCommon Core State Standards High School Geometry Constructions
ommon ore State Standards High School Geometry onstructions HSG.O..12 onstruction: opying a line segment HSG.O..12 onstruction: opying an angle HSG.O..12 onstruction: isecting a line segment HSG.O..12
More informationHonors Geometry Pacing Guide Honors Geometry Pacing First Nine Weeks
Unit Topic To recognize points, lines and planes. To be able to recognize and measure segments and angles. To classify angles and name the parts of a degree To recognize collinearity and betweenness of
More informationCourse: Geometry Level: Regular Date: 11/2016. Unit 1: Foundations for Geometry 13 Days 7 Days. Unit 2: Geometric Reasoning 15 Days 8 Days
Geometry Curriculum Chambersburg Area School District Course Map Timeline 2016 Units *Note: unit numbers are for reference only and do not indicate the order in which concepts need to be taught Suggested
More informationTerm Definition Figure
Geometry Unit 1 Packet  Language of Geometry Name: #: Video Notes LT 1.1  Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruent, parallel, perpendicular, etc.) Term
More information