M3.1 The Midpoint and Intercept theorems
|
|
- Arlene Perry
- 7 years ago
- Views:
Transcription
1 Methods 3.1 The Midpoint and Intercept theorems M3.1 The Midpoint and Intercept theorems efore you start ou should be able to: prove two triangles congruent prove two triangles similar use properties of similar triangles. Objective hy do this? rchitects have to have an excellentknowledge of geometry. Get Ready ou can understand the midpoint theorem and the intercept theorem. ou can use the midpoint theorem and the intercept theorem. 54 2x 2z a 84 x 54 2y 42 1 a The two triangles are similar explain why. b rite a in terms of x or y or z. 2 Solve these equations: a t b 5 s 4 9 Key oints The Intercept theorem The lines and cut a pair of parallel lines at, and, respectively. Then: The Midpoint theorem special case of the converse of the intercept theorem is the midpoint theorem. In the triangle, and are the midpoints of the sides and. Then the line is parallel to the side of the triangle and is equal to half its length. 1
2 hapter 3 The Midpoint and Intercept theorems Example 1 10 cm 4. Find the length of. This problem should be solved algebraically. Using the intercept theorem: Let the length of x cm. x x x 6(x 4.5) x Use the last two fractions with x and so x 4.5 Multiply through by 10(x 4.5) and cancel. Exercise 3 (ll diagrams not to scale) 1 9 cm 4 cm Find the length of cm 1 7 cm Find the length of. 3 Find the length of E. E 2
3 Methods 3.1 The Midpoint and Intercept theorems 4 2 cm 3 cm 3 cm 1 cm F E H a ork out the length of. c ork out the length of E. b ork out the length of FH. 5 is a rectangle. K, L, M and N are the midpoints of,, and respectively. Use the midpoint theorem to show that the quadrilateral KLMN is a parallelogram. 6 2 cm F E 2 cm a ork out the length of E. E b ork out the length of F. 7 kite has the property that its diagonals intersect at right angles. is a kite. E, F, G, H are the midpoints of the sides,, and respectively. rove that EFGH is a rectangle. 8 E is the midpoint of. E is parallel to. Show that: a area triangle E area triangle E b area triangle E : area triangle 1 : 2 9 is the midpoint of and is the midpoint of. and intersect at. rove that : 1 : 3 10 is a parallelogram. M is the midpoint of the diagonal and L is the midpoint of M. is the point on such that L is parallel to. is the point on such that L is parallel to. Find area L : area 3
4 hapter 3 The Midpoint and Intercept theorems M3.2 Intersecting hords efore you start ou should be able to: prove that two triangles are similar recall the angles in the same segment (or angles subtended at the circumference by equal arcs) theorem recall the properties of tangents to circles. Objectives hy do this? rchitects study the properties of circles so that they can design structures. Get Ready ou can solve problems which involve intersecting chords of circles. ou can solve problems which involve a chord and a tangent to a circle. 1 Show that the two triangles are similar. 2 Find the value of x. x cm 9 cm Key oints For any chords and intersecting inside a circle:. For any chords and intersecting outside a circle:. Let, and T be points on a circle. is the point of intersection of the tangent at T and the chord. T 2 T 4
5 Methods 3.2 Intersecting hords Example 2,, and are 4 points on a circle. and are straight lines. ork out the length of Use Example 3,, and are points on a circle. and are straight lines. 4 cm. 11 cm.. ork out the length of. 11 cm 4 cm cm Use Example 4, and are 3 points on a circle. is a straight line. is a tangent to the circle at.,. Find the length of. Let x cm x(x 5) 6 2 x 2 5x 36 0 Use 2 5 x 5 Expand the brackets and collect the terms on the left hand side. (x 9)(x 4) 0 x 9 or x 4 4, 9 Select the positive value of x. Solve by factorising or using the quadratic formula. Exercise 3 (ll diagrams not to scale) 1,, and are 4 points on a circle. and are straight lines. ork out the length of. 4 cm 5
6 hapter 3 The Midpoint and Intercept theorems 2,, and are 4 points on a circle. is the point of intersection of the chords and. ork out the length of. 9 cm 4 cm 3,, and are points on a circle. The chords and meet inside the circle at., 12 cm,. ork out the length of. 4 opy and complete the table for the given diagram. a b c d e f g h ,, and are 4 points on a circle. 23 cm.. ork out the length of. 12 cm 6,, and are 4 points on a circle. and are straight lines. a ork out the length of. b rite down the length of. 10 cm 6
7 Methods 3.2 Intersecting hords 7,, and are 4 points on a circle. 10 cm. ork out the length of. 8, and are points on a circle. a Show that x satisfies the equation x 2 30x 216 b Find the value of x. 12 cm 30 cm x cm 9,, and are 4 points on a circle. The lengths of some parts of the diagram are given in the table. opy and complete the table. a b c d e f g h O is the centre of the circle. O is a diameter. M M. 10 cm. OM 2 cm. Find the length of M. O M 7
8 hapter 3 The Midpoint and Intercept theorems 11 O is the centre of the circle. O is a diameter. M is the midpoint of. The radius of the circle is c cm. OM a cm. M b cm. Show that: c 2 a 2 b 2 O M 12 O is the centre of the circle. O is a diameter. M M. M 4 cm. OM. Find the length of. O M 13 In each of the cases copy and complete the table. T a 9 16 b 4 5 T c 10 5 d 8 16 e f g , and are 3 points on a circle, centre O, radius 4.. is a straight line. is a tangent to the circle at. ork out the length of O. O 4 cm 8
9 Methods 3.2 Intersecting hords 15, and T are 3 points on a circle. is a straight line. T is a tangent to the circle at T. a ork out the length of T. b Given that T is a diameter of the circle, work out the length of T. c ork out the length of T. 10 cm T 16, and are 3 points on a circle. is the tangent to the circle at. is a straight line. is a diameter. rove that 2 Review T T 2 9
10 hapter 3 The Midpoint and Intercept theorems nswers hapter 3 M3.1 Get Ready answers 1 a Missing angles in the triangles are 84 and 42 respectively. The triangles are similar because they are equiangular. b a z 2 a t 18 b s Exercise 3 answers cm a 3.2 cm b 9. c 4. 5 Join to. In triangle, KL is half of and parallel to. In triangle, MN is half of and parallel to. Hence KLMN is a parallelogram. 6 a 1.2 cm b Join to. EF is parallel to, HG is parallel to. Therefore EF is parallel to HG. Similarly HE is parallel to and GF. ut is perpendicular to, so HE is perpendicular to EF and EFGH is a rectangle. 8 a E E (E is the midpoint of ) and E is common. Since the triangles have the same base and the same height they have the same area. b Triangles and have equal bases and the same height ( is common). Hence, they have the same area. Hence, rea triangle E : area triangle 1 : 2 9 is parallel to ; angle angle, angle angle. Hence triangles and are similar. Now 1 so , so : 16 M3.2 Get Ready answers 1 The angles in the two triangles are equal in pairs (alternate angles and vertically opposite angles) 2 x 6.75 Exercise 3 answers cm cm 4 a b c d e f g h Let x x(23 x) x x 2 60 x 2 23x 60 0 x 3 or x cm 6 a b 27 cm x(x 30 ) x 2 30x 216 x 2 30x (x 36)(x 6) 0, x 36 or 6. Here x 6 9 a b c d e f g h (5 2) (5 2) 21 M 2 21 M (c a) (c a) M M b b So c 2 a 2 b 2 So c 2 a 2 b 2 12 M M M M (10 6) 4 M 2 M cm 10
11 nswers 13 T a b c d e f g (4 5) 36 6 O O a 8 18 T 2 T 12 cm b T T 180 cm c ( 180 ) T 80 cm 16 2 ( )
Geometry 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 informationCircle 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 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 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 informationBiggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
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 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 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 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 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 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 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 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 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 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 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 informationSituation: Proving Quadrilaterals in the Coordinate Plane
Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra
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 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 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 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 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 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 informationSTRAND: ALGEBRA Unit 3 Solving Equations
CMM Subject Support Strand: ALGEBRA Unit Solving Equations: Tet STRAND: ALGEBRA Unit Solving Equations TEXT Contents Section. Algebraic Fractions. Algebraic Fractions and Quadratic Equations. Algebraic
More informationCAMI Education linked to CAPS: Mathematics
- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
More informationAdvanced Euclidean Geometry
dvanced Euclidean Geometry What is the center of a triangle? ut what if the triangle is not equilateral?? Circumcenter Equally far from the vertices? P P Points are on the perpendicular bisector of a line
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 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 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 informationGeometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
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 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 informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
More information1. Find the length of BC in the following triangles. It will help to first find the length of the segment marked X.
1 Find the length of BC in the following triangles It will help to first find the length of the segment marked X a: b: Given: the diagonals of parallelogram ABCD meet at point O The altitude OE divides
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 information1 Solution of Homework
Math 3181 Dr. Franz Rothe February 4, 2011 Name: 1 Solution of Homework 10 Problem 1.1 (Common tangents of two circles). How many common tangents do two circles have. Informally draw all different cases,
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 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 informationConjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence - a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
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 informationAdditional Topics in Math
Chapter Additional Topics in Math In addition to the questions in Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math, the SAT Math Test includes several questions that are
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 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 III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
More information/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
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 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: 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 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 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 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 information11 th Annual Harvard-MIT Mathematics Tournament
11 th nnual Harvard-MIT Mathematics Tournament Saturday February 008 Individual Round: Geometry Test 1. [] How many different values can take, where,, are distinct vertices of a cube? nswer: 5. In a unit
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 informationTest on Circle Geometry (Chapter 15)
Test on Circle Geometry (Chapter 15) Chord Properties of Circles A chord of a circle is any interval that joins two points on the curve. The largest chord of a circle is its diameter. 1. Chords of equal
More informationWeek 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test
Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan
More informationLesson 2: Circles, Chords, Diameters, and Their Relationships
Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct
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 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 informationParallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.
CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes
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 informationEquation of a Line. Chapter H2. The Gradient of a Line. m AB = Exercise H2 1
Chapter H2 Equation of a Line The Gradient of a Line The gradient of a line is simpl a measure of how steep the line is. It is defined as follows :- gradient = vertical horizontal horizontal A B vertical
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 informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
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 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 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 informationChapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane
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 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 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 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 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 informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
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 informationArea of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
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. 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 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 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, 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 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 informationWORK SCHEDULE: MATHEMATICS 2007
, K WORK SCHEDULE: MATHEMATICS 00 GRADE MODULE TERM... LO NUMBERS, OPERATIONS AND RELATIONSHIPS able to recognise, represent numbers and their relationships, and to count, estimate, calculate and check
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 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 informationChapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
More informationof surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationCurriculum Overview YR 9 MATHS. SUPPORT CORE HIGHER Topics Topics Topics Powers of 10 Powers of 10 Significant figures
Curriculum Overview YR 9 MATHS AUTUMN Thursday 28th August- Friday 19th December SUPPORT CORE HIGHER Topics Topics Topics Powers of 10 Powers of 10 Significant figures Rounding Rounding Upper and lower
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 informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
More informationSection 1: How will you be tested? This section will give you information about the different types of examination papers that are available.
REVISION CHECKLIST for IGCSE Mathematics 0580 A guide for students How to use this guide This guide describes what topics and skills you need to know for your IGCSE Mathematics examination. It will help
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 informationMATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
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 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 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 informationMathematics. GCSE subject content and assessment objectives
Mathematics GCSE subject content and assessment objectives June 2013 Contents Introduction 3 Subject content 4 Assessment objectives 11 Appendix: Mathematical formulae 12 2 Introduction GCSE subject criteria
More informationThe Australian Curriculum Mathematics
The Australian Curriculum Mathematics Mathematics ACARA The Australian Curriculum Number Algebra Number place value Fractions decimals Real numbers Foundation Year Year 1 Year 2 Year 3 Year 4 Year 5 Year
More information" Angles ABCand DEFare congruent
Collinear points a) determine a plane d) are vertices of a triangle b) are points of a circle c) are coplanar 2. Different angles that share a common vertex point cannot a) share a common angle side! b)
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 information2, 3 1, 3 3, 2 3, 2. 3 Exploring Geometry Construction: Copy &: Bisect Segments & Angles Measure & Classify Angles, Describe Angle Pair Relationship
Geometry Honors Semester McDougal 014-015 Day Concepts Lesson Benchmark(s) Complexity Level 1 Identify Points, Lines, & Planes 1-1 MAFS.91.G-CO.1.1 1 Use Segments & Congruence, Use Midpoint & 1-/1- MAFS.91.G-CO.1.1,
More information