Lesson 12-13: Properties of Similarity Transformations
|
|
- Cecilia Lewis
- 6 years ago
- Views:
Transcription
1 Lesson 12-13: Properties of Similarity Transformations Learning Target I can define a similarity transformation as the composition of basic rigid motions and dilations. I can define two figures to be similar if there is a similarity transformation that takes one to the other. Opening Activity The diagram below shows a dilation of the plane or doesn t it? Explain your answer. Definition A similarity transformation (or similarity) is a composition of a number of and/or. The of a similarity transformation is the product of the scale factors of the dilations in the composition; if there are no dilations in the composition, the scale factor is defined to be 1. Characteristics Similar figures should look the same, but one is a,,, or relative to the other, corresponding angles are equal in measure Definition 2 Two figures in a plane are similar if there exists a taking one figure onto the other figure. Examples Similar Non-Examples
2 Example 1. Given triangle ABC as shown on the diagram of the coordinate plane. a) State the coordinates of all vertices of ABC. A B C b) Perform a translation so that vertex A maps to the origin. State this transformation in T a,b notation. State all new coordinates. A B C c) Next, dilate the image A B C from the origin using a scale factor of 1 3. State this with D P,r notation. State all new coordinates. A B C d) Without measuring, what is the ratio of A B : AB? e) Without measuring what can we say about angles ABC and A B C. What happens to angle measure after a similarity transformation? f) Finally, translate the image A B C so that the vertex A maps to the original point A. State the translation with T a,b notation. State all new coordinates. A B C g) Using transformations, describe how the resulting image A B C relates to the original figure ABC.
3 Example 2. Given the coordinate plane shown, identify a similarity transformation, if one exists, mapping X onto Y. Lesson Summary Two figures are similar if there exists a similarity transformation that maps one figure onto the other. A similarity transformation is a composition of a finite number of dilations or rigid motions. Properties of similarity transformations: There is a scale factor r for G, so that for any pair of points P and Q with images P = G(P) and Q = G(Q), then P Q = rpq. In other words, THE LENGTH OF A SIDE OF THE PRE-IMAGE IS MULTIPLIED BY THE SCALE FACTOR. A similarity transformation sends angles to angles of equal measure. In other words, CORRESPONDING ANGLES OF SIMILAR FIGURES ARE EQUAL.
4 Lesson 12-13: Properties of Similarity Transformations Classwork Exercise 1. A similarity transformation for triangle STU is described by r. Locate and label the image of STU under the similarity transformation D O, 1 r 2 y=x( STU) where the center of dilation is the origin. Original Coordinates ry = x D0, 1/2 S(, ) S (, ) S (, ) T(, ) T (, ) T (, ) U(, ) U (, ) U (, )
5 Exercise 2. Given O(0,0) and quadrilateral BCDE, with B( 5,1), C( 6, 1), D( 4, 1), and E( 4,2), what are the coordinates of the vertices of the image of BCDE under the similarity transformation r x axis (D O,3 (BCDE))? Original Coordinates D O,3 (BCDE) r x axis B(, ) B (, ) B (, ) C(, ) C (, ) C (, ) D(, ) D (, ) D (, ) E(, ) E (, ) E (, ) Exercise 3. Given the coordinate plane shown, identify a similarity transformation, if one exists, that maps ABCD onto A B C D. If one does not exist, explain why.
6 Exercise 4. A similarity transformation consists of a reflection over line l, followed by a dilation from O with a scale factor of r = 3 and result in G H I. 4 a) Find GH, IH, and IG in centimeters. Without measuring, calculate G H, I H and I G. b) m GIH = (4x + 19), m GHI = (3x 12), and m H G I = (x + 1). Find x and m G I H. Exercise 5. Similarity transformation G consists of a reflection across line l, followed by a dilation centered at P with scale factor r = 3. l If the original triangle had a perimeter of 16 units, what would the perimeter of the image be?
Classwork. Example 1 S.35
Classwork Example 1 In the picture below, we have a triangle AAAAAA that has been dilated from center OO by a scale factor of rr = 1. It is noted 2 by AA BB CC. We also have triangle AA BB CC, which is
More informationLesson 2B: Thales Theorem
Lesson 2B: Thales Theorem Learning Targets o I can identify radius, diameter, chords, central circles, inscribed circles and semicircles o I can explain that an ABC is a right triangle, then A, B, and
More information9. Yes; translate so that the centers align, and then dilate using the ratio of radii to map one circle to another.
9. Yes; translate so that the centers align, and then dilate using the ratio of radii to map one circle to another. 10. Keegan dilated using A as the center of dilation instead of the origin. Point A should
More informationLesson 5: The Graph of the Equation y = f(x)
Lesson 5: The Graph of the Equation y = f(x) Learning targets: I can identify when a function is increasing, decreasing, positive and negative and use interval notation to describe intervals where the
More information9.2. Length of Line Segments. Lesson Objectives. Find the lengths of line segments on the x-axis and y-axis.
9.2 Length of Line Segments Lesson Objectives Find lengths of horizontal and vertical line segments on the coordinate plane. Solve real-world problems involving coordinates and a coordinate plane. Learn
More informationG.CO.6-9 ONLY COMMON CORE QUESTIONS
Class: Date: G.CO.6-9 ONLY COMMON CORE QUESTIONS Multiple Choice Identify the choice that best completes the statement or answers the question. 1 The image of ABC after a rotation of 90º clockwise about
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'
More informationEnd of Course Review
End of Course Review Geometry AIR Test Mar 14 3:07 PM Test blueprint with important areas: Congruence and Proof 33 39% Transformations, triangles (including ASA, SAS, SSS and CPCTC), proofs, coordinate/algebraic
More informationSOLUTION. Taken together, the preceding equations imply that ABC DEF by the SSS criterion for triangle congruence.
1. [20 points] Suppose that we have ABC and DEF in the Euclidean plane and points G and H on (BC) and (EF) respectively such that ABG DEH and AGC DHF. Prove that ABC DEF. The first congruence assumption
More informationMathematics Curriculum
Common Core Mathematics Curriculum Table of Contents 1 Similarity GRADE 8 MODULE 3 Module Overview... 2 Topic A: Dilation (8.G.A.3)... 7 Lesson 1: What Lies Behind Same Shape?... 9 Lesson 2: Properties
More informationName Geometry Common Core Regents Review Packet - 3. Topic 1 : Equation of a circle
Name Geometry Common Core Regents Review Packet - 3 Topic 1 : Equation of a circle Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( ) 1. The endpoints of a diameter
More information12 Rigid Transformations
www.ck12.org CHAPTER 12 Rigid Transformations Chapter Outline 12.1 EXPLORING SYMMETRY 12.2 TRANSLATIONS AND VECTORS 12.3 REFLECTIONS 12.4 ROTATIONS 12.5 COMPOSITION OF TRANSFORMATIONS 12.6 EXTENSION: TESSELLATIONS
More informationa. Do you think the function is linear or non-linear? Explain using what you know about powers of variables.
8.5.8 Lesson Date: Graphs of Non-Linear Functions Student Objectives I can examine the average rate of change for non-linear functions and learn that they do not have a constant rate of change. I can determine
More informationLesson 26: Characterization of Parallel Lines
Student Outcomes Students know that when a system of linear equations has no solution, i.e., no point of intersection of the lines, then the lines are parallel. Lesson Notes The discussion that begins
More informationGeometry AIR Test. Mar 14-3:07 PM. coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula.
Geometry AIR Test Mar 14-3:07 PM Congruence and Proof 33-39% coordinate/algebraic proofs, parallel and perpendicular lines, distance formula, midpoint formula. missing sides on triangles (trig ratios,
More informationStudent Outcomes. Lesson Notes. Classwork. Opening Exercise (5 minutes)
Student Outcomes Students know that truncated cones and pyramids are solids obtained by removing the top portion above a plane parallel to the base. Students find the volume of truncated cones. Lesson
More informationStudent Outcomes. Lesson Notes. Classwork. Example 1 (5 minutes) Students apply knowledge of geometry to writing and solving linear equations.
Student Outcomes Students apply knowledge of geometry to writing and solving linear equations. Lesson Notes All of the problems in this lesson relate to what students have learned about geometry in recent
More informationMEP Pupil Text 13-19, Additional Material. Gradients of Perpendicular Lines
Graphs MEP Pupil Text -9, Additional Material.B Gradients of Perpendicular Lines In this section we explore the relationship between the gradients of perpendicular lines and line segments. Worked Example
More information6 th Grade Math Connects
6 th Grade Math Connects Chapter 1: Multiply and Divide Decimals Multi-Part Lesson 1: Multiply Decimals A: Estimate Products B: Explore Multiply Decimals by Whole Numbers C: Multiply Decimals by Whole
More informationUnit 4A Part B 1) The radius of a circular clock face is 13 centimeters. Which expression can be used to find the
7.5B 1) The radius of a circular clock face is 13 centimeters. Which expression can be used to find the circumference of the clock face in centimeters? F. G. 2) Information about three circles is listed
More informationSTRAND J: TRANSFORMATIONS, VECTORS and MATRICES
Mathematics SKE, Strand J STRAND J: TRANSFORMATIONS, VECTORS and MATRICES J4 Matrices Text Contents * * * * Section J4. Matrices: Addition and Subtraction J4.2 Matrices: Multiplication J4.3 Inverse Matrices:
More informationMidterm Review Packet. Geometry: Midterm Multiple Choice Practice
: Midterm Multiple Choice Practice 1. In the diagram below, a square is graphed in the coordinate plane. A reflection over which line does not carry the square onto itself? (1) (2) (3) (4) 2. A sequence
More informationUnit 1. GSE Analytic Geometry EOC Review Name: Units 1 3. Date: Pd:
GSE Analytic Geometry EOC Review Name: Units 1 Date: Pd: Unit 1 1 1. Figure A B C D F is a dilation of figure ABCDF by a scale factor of. The dilation is centered at ( 4, 1). 2 Which statement is true?
More informationChapter 3 Summary 3.1. Determining the Perimeter and Area of Rectangles and Squares on the Coordinate Plane. Example
Chapter Summar Ke Terms bases of a trapezoid (.) legs of a trapezoid (.) composite figure (.5).1 Determining the Perimeter and Area of Rectangles and Squares on the Coordinate Plane The perimeter or area
More informationReteaching , or 37.5% 360. Geometric Probability. Name Date Class
Name ate lass Reteaching Geometric Probability INV 6 You have calculated probabilities of events that occur when coins are tossed and number cubes are rolled. Now you will learn about geometric probability.
More informationLesson 29: Solving Radical Equations
Lesson 29: Solving Radical Equations Student Outcomes Students develop facility in solving radical equations. Lesson Notes In the previous lesson, students were introduced to the notion of solving radical
More informationGeo-Activity. 1 Draw a triangle. Label it TPQR. Choose a point C outside the triangle. P on CP&*(such that CP 2 p CP. Locate Q and R the same way.
age 1 of 7. Dilations Goal Identify and draw dilations. Key Words dilation reduction enlargement Geo-Activity Drawing a Dilation 1 Draw a triangle. Label it TQ. hoose a point outside the triangle. 2 Use
More informationChapter 2. EXPLORING LINEAR RELATIONS
Chapter 2. EXPLORING LINEAR RELATIONS In this chapter we begin with a review of proportional relationships as discussed in seventh grade mathematics. In eighth grade we focus on the unit rate of change
More information2-7 Applications of Proportions. Warm Up. Evaluate each expression for a = 3, b = 2, c = a b 2. 3b ab 2c. Solve each proportion
Warm Up Evaluate each expression for a = 3, b = 2, c = 5. 1. 4a b 2. 3b 2 5 3. ab 2c Solve each proportion. 4. 5. Learning Goal 1. Students will use ratios to find missing measures of similar figures 2.
More informationMathematics Success Grade 6
T632 Mathematics Success Grade 6 [OBJECTIVE] The students will draw polygons in the coordinate plane given the coordinates for the vertices and use the coordinates to find the length of the sides in mathematical
More informationPage 1 of 11 Name: 1) Which figure always has exactly four lines of reflection that map the figure onto itself? A) rectangle B) square C) regular octagon D) equilateral triangle ee4caab3 - Page 1 2) In
More informationJANE LONG ACADEMY HIGH SCHOOL MATH SUMMER PREVIEW PACKET SCHOOL YEAR. Geometry
JANE LONG ACADEMY HIGH SCHOOL MATH SUMMER PREVIEW PACKET 2015-2016 SCHOOL YEAR Geometry STUDENT NAME: THE PARTS BELOW WILL BE COMPLETED ON THE FIRST DAY OF SCHOOL: DUE DATE: MATH TEACHER: PERIOD: Algebra
More informationPRACTICE TEST ANSWER KEY & SCORING GUIDELINES INTEGRATED MATHEMATICS I
Ohio s State Tests PRACTICE TEST ANSWER KEY & SCORING GUIDELINES INTEGRATED MATHEMATICS I Table of Contents Questions 1 29: Content Summary and Answer Key... iii Question 1: Question and Scoring Guidelines...
More information7.1 Projections and Components
7. Projections and Components As we have seen, the dot product of two vectors tells us the cosine of the angle between them. So far, we have only used this to find the angle between two vectors, but cosines
More informationThe WhatPower Function à An Introduction to Logarithms
Classwork Work with your partner or group to solve each of the following equations for x. a. 2 # = 2 % b. 2 # = 2 c. 2 # = 6 d. 2 # 64 = 0 e. 2 # = 0 f. 2 %# = 64 Exploring the WhatPower Function with
More informationConcepts. Materials. Objective
. Activity 10 From a Distance... You Can See It! Teacher Notes Concepts Midpoint between two points Distance between two points Pythagorean Theorem Calculator Skills Entering fractions: N Setting decimal
More informationRight Triangles
30 60 90 Right Triangles The 30-60 -90 triangle is another special triangle. Like the 45-45 -90 triangle, properties of the 30-60 -90 triangle can be used to find missing measures of a triangle if the
More informationAnswers to Course 3 Unit 3 Practice
Answers to Course 3 Unit 3 Practice Lesson 1-1 1. a. 75; 15 b. 53; 13 c. 19; 19 d. 7; 117 e. (9 ); (1 ). a. ; b..5; 3.5 c. 3; 5 d. 33; 57 e. 5; 5 3. a. 7.5; 17.5 b. 31.5; 1.5 c. 5; 135 d. 59; 11 e. 1.;
More informationUsing the Zero Product Property to Find Horizontal Intercepts
LESSON 11 Using the Zero Product Property to Find Horizontal Intercepts LEARNING OBJECTIVES Today I am: exploring what happens when two factors have a product of 0. So that I can: solve equations that
More informationTest Corrections for Unit 1 Test
MUST READ DIRECTIONS: Read the directions located on www.koltymath.weebly.com to understand how to properly do test corrections. Ask for clarification from your teacher if there are parts that you are
More informationHow can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots
. Approximating Square Roots How can you find decimal approximations of square roots that are not rational? ACTIVITY: Approximating Square Roots Work with a partner. Archimedes was a Greek mathematician,
More informationUNIT 5 QUADRATIC FUNCTIONS Lesson 1: Interpreting Structure in Expressions Instruction
Prerequisite Skills This lesson requires the use of the following skills: evaluating expressions using the order of operations evaluating expressions for a given value identifying parts of an expression
More informationIdentity and Inverse Matrices
Identity and Inverse Matrices Booklet Four Copyright 207 Robert E. Mason IV. All Rights Reserved. 2 Prepared by Dr. Robert E. Mason IV Mathematics Consultant 3 4 Identity and Inverse Matrices Objectives
More informationACTIVITY: Factoring Special Products. Work with a partner. Six different algebra tiles are shown below.
7.9 Factoring Special Products special products? How can you recognize and factor 1 ACTIVITY: Factoring Special Products Work with a partner. Six different algebra tiles are shown below. 1 1 x x x 2 x
More informationWhich statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''?
Unit 2 Review 1. Parallelogram FGHJ was translated 3 units down to form parallelogram F 'G'H'J '. Parallelogram F 'G'H'J ' was then rotated 90 counterclockwise about point G' to obtain parallelogram F
More informationUnit 5: Applying Similarity of Triangles
Unit 5: Applying Similarity of Triangles Lesson 2: Applying the Triangle Side Splitter Theorem and Angle Bisector Theorem Students understand that parallel lines cut transversals into proportional segments.
More informationChetek-Weyerhaeuser High School/Middle School
Chetek-Weyerhaeuser High School/Middle School Unit 1 Foundations Math RtI 8 Units and s Math RtI 8 s 1. I can add and subtract fractions with like and unlike denominators. I can add and subtract fractions
More informationMathwithsheppard.weebly.com
Unit #: Powers and Polynomials Unit Outline: Date Lesson Title Assignment Completed.1 Introduction to Algebra. Discovering the Exponent Laws Part 1. Discovering the Exponent Laws Part. Multiplying and
More informationLesson 28: Another Computational Method of Solving a Linear System
Lesson 28: Another Computational Method of Solving a Linear System Student Outcomes Students learn the elimination method for solving a system of linear equations. Students use properties of rational numbers
More information2, find c in terms of k. x
1. (a) Work out (i) 8 0.. (ii) 5 2 1 (iii) 27 3. 1 (iv) 252.. (4) (b) Given that x = 2 k and 4 c 2, find c in terms of k. x c =. (1) (Total 5 marks) 2. Solve the equation 7 1 4 x 2 x 1 (Total 7 marks)
More informationALGEBRA 1. Interactive Notebook Chapter 2: Linear Equations
ALGEBRA 1 Interactive Notebook Chapter 2: Linear Equations 1 TO WRITE AN EQUATION: 1. Identify the unknown (the variable which you are looking to find) 2. Write the sentence as an equation 3. Look for
More informationAnswers to Geometry Unit 3 Practice
Lesson 17-1 1. a. (4, 9) b. (8, 0) c. (, 1) d. 9, e. (0.10,.). a. b. Aʹ(4., 4.), Bʹ(6, 7.), Cʹ(9, 0), Dʹ(6, 6). C 4. a. b. enlargement c. (1, ) d. Pʹ(7, 10), Qʹ(9, 4), Rʹ(, 6). Aʹ(, 7.), Bʹ(, 7.), Cʹ(,
More informationCollecting Like Terms
MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.
More informationPeriod: Date: Lesson 3B: Properties of Dilations and Equations of lines
Name: Period: Date: : Properties of Dilations and Equations of lines Learning Targets I can identify the properties of dilation mentioned as followed: dilation takes a line not passing through the center
More information8 th Grade Math Connects
8 th Grade Math Connects Chapter 1: Rational Numbers and Percent Multi-Part Lesson 1: Rational Numbers A: Rational Numbers B: Add and Subtract Rational Numbers C: Multiply Rational Numbers D: Divide Rational
More information0615geo. Geometry CCSS Regents Exam In the diagram below, congruent figures 1, 2, and 3 are drawn.
0615geo 1 Which object is formed when right triangle RST shown below is rotated around leg RS? 4 In the diagram below, congruent figures 1, 2, and 3 are drawn. 1) a pyramid with a square base 2) an isosceles
More informationVectors - Applications to Problem Solving
BERKELEY MATH CIRCLE 00-003 Vectors - Applications to Problem Solving Zvezdelina Stankova Mills College& UC Berkeley 1. Well-known Facts (1) Let A 1 and B 1 be the midpoints of the sides BC and AC of ABC.
More informationTest Review: Geometry I Period 3,5,7. ASSESSMENT DATE: Wednesday 3/25 (FOR ALL CLASSES) Things it would be a good idea to know:
Test Review: Geometry I Period 3,5,7 ASSESSMENT DATE: Wednesday 3/25 (FOR ALL CLASSES) Things it would be a good idea to know: 1) How to create proportions from a. a word problem b. a pair of similar triangles
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
EOCT Practice Items 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B'
More informationExpress g(x) in the form f(x) + ln a, where a (4)
SL 2 SUMMER PACKET PRINT OUT ENTIRE PACKET, SHOW YOUR WORK FOR ALL EXERCISES ON SEPARATE PAPER. MAKE SURE THAT YOUR WORK IS NEAT AND ORGANIZED. WORK SHOULD BE COMPLETE AND READY TO TURN IN THE FIRST DAY
More informationFactorizing Algebraic Expressions
1 of 60 Factorizing Algebraic Expressions 2 of 60 Factorizing expressions Factorizing an expression is the opposite of expanding it. Expanding or multiplying out a(b + c) ab + ac Factorizing Often: When
More informationSUMMER WORK 2017 Name:
SUMMER WORK 2017 Name: SUMMER WORK is due at the beginning of class on the FIRST DAY OF SCHOOL. It is graded! Welcome to Accelerated GSE Geometry B/Algebra II at Whitewater High School. We are excited
More informationproportion, p. 163 cross product, p. 168 scale drawing, p. 170
REVIEW KEY VOCABULARY classzone.com Multi-Language Glossary Vocabulary practice inverse operations, p. 14 equivalent equations, p. 14 identity, p. 156 ratio, p. 162 proportion, p. 16 cross product, p.
More informationGEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent?
GEO REVIEW TEST #1 Name: Date: 1. In which quadrilateral are the diagonals always congruent? (1) rectangle (3) rhombus 4. In the accompanying diagram, lines AB and CD intersect at point E. If m AED = (x+10)
More information3.5. Did you ever think about street names? How does a city or town decide what to. composite figures
.5 Composite Figures on the Coordinate Plane Area and Perimeter of Composite Figures on the Coordinate Plane LEARNING GOALS In this lesson, ou will: Determine the perimeters and the areas of composite
More informationVisit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths
Exercise 1.1 1. Find the area of a triangle whose sides are respectively 150 cm, 10 cm and 00 cm. The triangle whose sides are a = 150 cm b = 10 cm c = 00 cm The area of a triangle = s(s a)(s b)(s c) Here
More informationSolutions to the Olympiad Maclaurin Paper
s to the Olympiad Maclaurin Paper M1. The positive integer N has five digits. The six-digit integer Pis formed by appending the digit 2 to the front of N. The six-digit integer Q is formed by appending
More informationMathematics Test Book 1. Grade8
Mathematics Test Book 1 Grade8 May 5 7, 2010 21656 1 Simplify the expression below. 12ab 8ab 5ab 3ab 25ab 25(3ab) 25 1 ab g g g 2 In the diagram below, AB CD, and EF intersects both lines. E A y B C 30
More informationObjectives To find the measure of an inscribed angle To find the measure of an angle formed by a tangent and a chord
1-3 Inscribed ngles ommon ore State Standards G-.. Identify and describe relationships among inscribed angles, radii, and chords. lso G-..3, G-..4 M 1, M 3, M 4, M 6 bjectives To find the measure of an
More information2.4 Investigating Symmetry
Locker LESSON 2.4 Investigating Symmetry Texas Math Standards The student is expected to: G.3.D Identify and distinguish between reflectional and rotational symmetry in a plane figure. Mathematical Processes
More informationLesson 9.3 Relating Congruent and Similar Figures to Geometric Transformations
Lesson 9. Relating ongruent and Similar Figures to Geometric Transformations State whether the figure and image are congruent or similar.. Rectangle D is rotated 90 clockwise about verte.. parallelogram
More information411 SAT ALGEBRA AND GEOMETRY QUESTIONS
SAT ALGEBRA AND GEOMETRY QUESTIONS SAT ALGEBRA AND GEOMETRY QUESTIONS NEW YORK Copyright 00 LearningExpress, LLC. All rights reserved under International and Pan-American Copyright Conventions. Published
More informationGSE Accelerated Geometry B/Algebra II SUMMER WORK 2018
GSE Accelerated Geometry B/Algebra II SUMMER WORK 2018 SUMMER WORK is due at the beginning of class on the FIRST DAY OF SCHOOL. It will be graded! Welcome to GSE Accelerated Geometry B/Algebra II at Whitewater
More informationExpress g(x) in the form f(x) + ln a, where a (4)
SL 2 SUMMER PACKET 2013 PRINT OUT ENTIRE PACKET, SHOW YOUR WORK FOR ALL EXERCISES ON SEPARATE PAPER. MAKE SURE THAT YOUR WORK IS NEAT AND ORGANIZED. WORK SHOULD BE COMPLETE AND READY TO TURN IN THE FIRST
More informationA Series Transformations
.3 Constructing Rotations We re halfway through the transformations and our next one, the rotation, gives a congruent image just like the reflection did. Just remember that a series of transformations
More informationIndicate whether the statement is true or false.
PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.
More informationThe symmetric group R + :1! 2! 3! 1. R :1! 3! 2! 1.
Chapter 2 The symmetric group Consider the equilateral triangle. 3 1 2 We want to describe all the symmetries, which are the motions (both rotations and flips) which takes the triangle to itself. First
More information5-7 The Pythagorean Theorem
5-7 The Pythagorean Theorem Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Classify each triangle by its angle measures. 1. 2. acute right 3. Simplify 12 4. If a = 6, b = 7, and c = 12, find
More informationSample Question Paper Mathematics First Term (SA - I) Class IX. Time: 3 to 3 ½ hours
Sample Question Paper Mathematics First Term (SA - I) Class IX Time: 3 to 3 ½ hours M.M.:90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided
More information1 What is the solution of the system of equations graphed below? y = 2x + 1
1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x
More informationEC and AB because AIA are congruent Substituting into the first equation above
4.1 Triangles Sum onjectures uxillary line: an extra line or segment that helps you with your proof. Page 202 Paragraph proof explaining why the Triangle Sum onjecture is true. onjecture: The sum of the
More informationEnd Of Term 2 Revision Sheet
Egyptian British International School Math Department Name:. Year (8..) End Of Term 2 Revision Sheet * Answer The following questions after revising your classwork copybook, course book, homework book
More informationin Trigonometry Name Section 6.1 Law of Sines Important Vocabulary
Name Chapter 6 Additional Topics in Trigonometry Section 6.1 Law of Sines Objective: In this lesson you learned how to use the Law of Sines to solve oblique triangles and how to find the areas of oblique
More informationKevin Delahoy dela6225@fredonia.edu Talena Baideme baid7981@fredonia.edu Introduction to Coordinate Geometry Introduction: Before students learn the slope of a line, teachers introduce coordinate geometry
More informationTransforming to a New Level!
Lesson.1 Assignment Name Date Transforming to a New Level! Using Transformations to Determine Area 1. Franco translates rectangle JKLM so that it has one verte on the origin. The result is rectangle J9K9L9M9.
More information6-3 Tests for Parallelograms. Determine whether each quadrilateral is a parallelogram. Justify your answer.
1. Determine whether each quadrilateral is a Justify your answer. 3. KITES Charmaine is building the kite shown below. She wants to be sure that the string around her frame forms a parallelogram before
More informationCHAPTER 5 : THE STRAIGHT LINE
EXERCISE 1 CHAPTER 5 : THE STRAIGHT LINE 1. In the diagram, PQ is a straight line. P 4 2 4 3 2 1 0 1 2 2 2. Find (a) the -intercept, (b) the gradient, of the straight line. Q (5,18) Q Answer :a).. b) 3
More informationGrade 7/8 Math Circles November 15 & 16, Areas of Triangles
Faculty of Mathematics Waterloo, Ontario NL 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles November 15 & 16, 016 Areas of Triangles In today s lesson, we are going to learn
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Wednesday, June 19, 00 1:15 to 4:15 p.m., only Notice... Scientific calculators
More informationLesson 12. Student Outcomes. Classwork. Opening Exercise (4 minutes) Discussion (4 minutes)
Student Outcomes Students are introduced to the formal process of solving an equation: starting from the assumption that the original equation has a solution. Students explain each step as following from
More informationQUADRATIC EQUATIONS EXPECTED BACKGROUND KNOWLEDGE
6 QUADRATIC EQUATIONS In this lesson, you will study aout quadratic equations. You will learn to identify quadratic equations from a collection of given equations and write them in standard form. You will
More informationShape Perimeter Area. + s 3. + s 2. side 3 (s 3 ) base (b) and side 1 (s 1
Geometric Formulas Reteaching 91 Math Course 1, Lesson 91 Shape Perimeter Area Square P = 4s A = s 2 Rectangle P = 2l + 2w A = lw Parallelogram P = 2b + 2s A = bh Triangle P = s 1 + s 2 + s 3 A = 1 2 bh
More informationAlgebra 1B notes and problems March 12, 2009 Factoring page 1
March 12, 2009 Factoring page 1 Factoring Last class, you worked on a set of problems where you had to do multiplication table calculations in reverse. For example, given the answer x 2 + 4x + 2x + 8,
More informationProperties of surfaces II: Second moment of area
Properties of surfaces II: Second moment of area Just as we have discussing first moment of an area and its relation with problems in mechanics, we will now describe second moment and product of area of
More informationLesson 8: Classwork. Exercises S.53
: Classwork Exercises. A function has the rule so that each input of x is assigned an output of x. a. Do you think the function is linear or nonlinear? Explain. b. Develop a list of inputs and outputs
More informationMath 8. Unit 8 Transformations Unit 9 Angles Unit 10 Geometry Unit 11 Scientific Notation. Name Teacher Period
Math 8 Unit 8 Transformations Unit 9 Angles Unit 10 Geometry Unit 11 Scientific Notation Name Teacher Period 1 Unit 8 Transformations Date Lesson Topic 1 Translations 2 Reflection 3 Reflection 4 Rotations
More informationHow can you factor the trinomial x 2 + bx + c into the product of two binomials? ACTIVITY: Finding Binomial Factors
7.7 Factoring x 2 + bx + c How can you factor the trinomial x 2 + bx + c into the product of two binomials? 1 ACTIVITY: Finding Binomial Factors Work with a partner. Six different algebra tiles are shown
More informationLesson 12: Overcoming Obstacles in Factoring
Lesson 1: Overcoming Obstacles in Factoring Student Outcomes Students factor certain forms of polynomial expressions by using the structure of the polynomials. Lesson Notes Students have factored polynomial
More informationLesson 23: The Defining Equation of a Line
Student Outcomes Students know that two equations in the form of and graph as the same line when and at least one of or is nonzero. Students know that the graph of a linear equation, where,, and are constants
More informationTRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions
CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)
More information