Study Guide: Similarity and Dilations
|
|
|
- Shanna Lindsey
- 5 years ago
- Views:
Transcription
1 Study Guide: Similarity and ilations ilations dilation is a transformation that moves a point a specific distance from a center of dilation as determined by the scale factor (r). Properties of ilations ilations map lines to lines, segments to segments, angles to angles, and rays to rays. The length of a line segment dilated from a center is equal to the length of the original line segment multiplied by the scale factor ( P! Q! = r PQ ). The above bullet point means that corresponding line segments are proportional. Corresponding angles of dilated objects are congruent. scale factor greater than 1 r > 1 will push out the dilated point from the center of dilation. scale factor less than 1 r < 1 will pull in the dilated point toward the center of dilation. If you dilate a line segment from the same center, the dilated line will either collinear or parallel. Example: O In this example, the original diamond is in the middle. It is dilated from center O by a scale factor of (approx.)! to generate.! is dilated from center O by a scale factor of (approx.) 2 to generate. 1
2 ILTIONS ON COORINTE PLNE Performing dilations can be easier if you use a coordinate plane. RULE: If center of dilation is (0,0), and scale factor is r, then the dilation of (x, y) is!, located at (rx, ry). RULE IN WORS: If your center of dilation is the origin, simply multiply the original coordinates by the scale factor to find the coordinates of the dilated point. What if your center of dilation is NOT the origin? In this case, you ll need to measure the horizontal and vertical distance from the center of dilation and multiply by the scale factor to determine the distance of the dilated point from the center of dilation. When given two similar shapes, you can locate the center of dilation (and determine the scale factor) by drawing rays that go through all corresponding points. The common point of intersection for all rays is the center of dilation. Example: Center of dilation at origin: The solid shape has been dilated by a scale factor of 3/2 from the origin to produce the dashed shape. Example: Center NOT at the origin: The solid shape has been dilated by a scale factor of 2 from point (13, 5) to produce the dashed shape. 2
3 Fundamental Theorem of Similarity The Fundamental Theorem of Similarity makes two primary conclusions: 1. When you dilate points P and Q from a center O, and the three points are NOT collinear, then the line segment PQ and the dilated line segment P Q are parallel. 2. Furthermore, the length of the P Q is equal to the length of PQ multiplied by the scale factor. In symbols: P! Q! = r PQ. Similarity thru rigid motions ilations alone might not be enough to prove that two shapes are similar. Often times, you ll need to perform a rotation or reflection first before doing your dilation. Pay close attention to the orientation N coordinate points of corresponding shapes when trying to determine the sequence of rigid motions. Example: C C C To dilate from C to either C or C, we need a sequence of rigid motions N dilations. 3
4 Ways to Prove Triangles similar You can prove that two triangles can be similar to each other by showing that: ngle-ngle Similarity: When two pairs of corresponding angle measures are equal, two triangles are similar If the lengths of corresponding side are proportional, two triangles are similar S--S similarity. If a corresponding angle is congruent and the two sides that form that angle have a directly proportional relationship, the triangles are similar. 52 4
5 PROLEM SET (Complete these problems before you submit your assessment for grading). ilate each object based on the directions. ilate from Center O by a Scale Factor of! and then a Scale Factor of 2.! X O Y Z ilate from Center O by a Scale Factor of 3. O riefly describe the process for dilating by a scale factor of 2 using a compass. 5
6 ilate according the instructions. ilate the shape from the center of dilation at (2, -8) by scale factors of 2 and 3. E C ilate TRI from the center of dilation at ( 9, 1) by scale factors of!! and!!. I T T T R T 6
7 Shapes,, C, and are similar. Identify at least 4 dilations, noting centers of dilation and scale factors for each dilation. C Shapes E, F, G, and H are similar. Identify at least 4 dilations, noting centers of dilation and scale factors for each dilation. F G H E
8 ilate the following Find and when and are dilated from the origin by a scale factor of!!. lso, find the length of!. and are dilations from the origin with a scale factor of!. Find and and! the find the length of. escribe the sequence of transformations that would map one shape to the other. C C 8
9 O O!!!! =? O!!!!!! = 14 O!!!! = 3.2 O!!!!!! =?!!!! = 5!!!!!!!! = Suppose and are parallel. Is O similar to O? Explain. 2. What is the length of O? 3. What is the length of O? Z Z X X Y Y 1. Is XYZ similar to X Y Z. Explain. 2. Find the length of YZ. 9
1. Figure A' is similar to Figure A. Which transformations compose the similarity transformation that maps Figure A onto Figure A'?
Exit Ticket Sample Solutions 1. Figure A' is similar to Figure A. Which transformations compose the similarity transformation that maps Figure A onto Figure A'? Figure A Figure A' We first take a dilation
Lesson 3A. Opening Exercise. Identify which dilation figures were created using r = 1, using r > 1, and using 0 < r < 1.
: Properties of Dilations and Equations of lines Opening Exercise Identify which dilation figures were created using r = 1, using r > 1, and using 0 < r < 1. : Properties of Dilations and Equations of
Unit 7 Scale Drawings and Dilations
Unit 7 Scale Drawings and Dilations Day Classwork Day Homework Friday 12/1 Unit 6 Test Monday 12/4 Tuesday 12/5 Properties of Scale Drawings Scale Drawings Using Constructions Dilations and Scale Drawings
Lesson 1: Introductions to Dilations
: Introductions to Dilations Learning Target I can create scale drawings of polygonal figures I can write scale factor as a ratio of two sides and determine its numerical value A dilation is a transformation
HANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273)
HANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.3 8.G.4
Grade 8 Module 3 Lessons 1 14
Eureka Math 2015 2016 Grade 8 Module 3 Lessons 1 14 Eureka Math, A Story of R a t i o s Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced, distributed,
Before How does the painting compare to the original figure? What do you expect will be true of the painted figure if it is painted to scale?
Dilations LAUNCH (7 MIN) Before How does the painting compare to the original figure? What do you expect will be true of the painted figure if it is painted to scale? During What is the relationship between
Eureka Math. Grade, Module. Student _B Contains Sprint and Fluency, Exit Ticket, and Assessment Materials
A Story of Eureka Math Grade, Module Student _B Contains Sprint and Fluency,, and Assessment Materials Published by the non-profit Great Minds. Copyright 2015 Great Minds. All rights reserved. No part
UNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS
UNDERSTAND SIMILARITY IN TERMS OF SIMILARITY TRANSFORMATIONS KEY IDEAS 1. A dilation is a transformation that makes a figure larger or smaller than the original figure based on a ratio given by a scale
Lesson 1: Scale Drawings
Name: : Scale Drawings Learning Target I can create scale drawings of polygonal figures by the Ratio Method I can determine the distance a point moves from the center of dilation based on the scale factor
8.G.A.3 Effects of Dilations on Length, Area, and Angles
8.G..3 Effects of Dilations on Length, rea, and ngles lignments to ontent Standards: 8.G..3 Task onsider triangle. a. Draw a dilation of with: i. enter and scale factor. ii. enter and scale factor 3. iii.
Lesson 4: Fundamental Theorem of Similarity (FTS)
Student Outcomes Students experimentally verify the properties related to the Fundamental Theorem of Similarity (FTS). Lesson Notes The goal of this activity is to show students the properties of the Fundamental
8 th Grade Domain 3: Geometry (28%)
8 th Grade Domain 3: Geometry (28%) 1. XYZ was obtained from ABC by a rotation about the point P. (MGSE8.G.1) Which indicates the correspondence of the vertices? A. B. C. A X, B Y, C Z A Y, B Z, C X A
Locus Locus. Remarks
4 4. The locus of a point is the path traced out by the point moving under given geometrical condition (or conditions). lternatively, the locus is the set of all those points which satisfy the given geometrical
1. What term describes a transformation that does not change a figure s size or shape?
1. What term describes a transformation that does not change a figure s size or shape? () similarity () isometry () collinearity (D) symmetry For questions 2 4, use the diagram showing parallelogram D.
6.1 Justifying Constructions
Name lass ate 6.1 Justifying onstructions Essential Question: How can you be sure that the result of a construction is valid? Resource Locker Explore 1 Using a Reflective evice to onstruct a erpendicular
Geometry Vocabulary Book
Geometry Vocabulary Book Units 2-4 Page 1 Unit 2 General Geometry Point Characteristics: Line Characteristics: Plane Characteristics: RELATED POSTULATES: Through any two points there exists exactly one
Lesson 4: Fundamental Theorem of Similarity (FTS)
Student Outcomes Students experimentally verify the properties related to the fundamental theorem of similarity (FTS). Lesson Notes The goal of this activity is to show students the properties of the fundamental
Target 5.4: Use angle properties in triangles to determine unknown angle measurements 5.4: Parallel Lines and Triangles
Unit 5 Parallel and Perpendicular Lines Target 5.1: Classify and identify angles formed by parallel lines and transversals 5.1 a Parallel and Perpendicular lines 5.1b Parallel Lines and its Angle Relationships
Unit 4, Activity 1, Vocabulary Self-Awareness
Unit 4, Activity 1, Vocabulary Self-Awareness Word/Phrase + Definition/Rule Example rigid (rigid motion) non-rigid (non-rigid motion) orientation isometry reflection line of reflection translation rotation
Unit 6 Quadrilaterals
Unit 6 Quadrilaterals ay lasswork ay Homework Monday Properties of a Parallelogram 1 HW 6.1 11/13 Tuesday 11/14 Proving a Parallelogram 2 HW 6.2 Wednesday 11/15 Thursday 11/16 Friday 11/17 Monday 11/20
Hands-On Explorations of Plane Transformations
Hands-On Explorations of Plane Transformations James King University of Washington Department of Mathematics king@uw.edu http://www.math.washington.edu/~king The Plan In this session, we will explore exploring.
Step 2: Extend the compass from the chosen endpoint so that the width of the compass is more than half the distance between the two points.
Student Name: Teacher: Date: District: Miami-Dade County Public Schools Test: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the given
Ch. 3 Parallel and Perpendicular Lines
Ch. 3 Parallel and Perpendicular Lines Section 3.1 Lines and Angles 1. I CAN identify relationships between figures in space. 2. I CAN identify angles formed by two lines and a transversal. Key Vocabulary:
Constructions. Unit 9 Lesson 7
Constructions Unit 9 Lesson 7 CONSTRUCTIONS Students will be able to: Understand the meanings of Constructions Key Vocabulary: Constructions Tools of Constructions Basic geometric constructions CONSTRUCTIONS
3. Given the similarity transformation shown below; identify the composition:
Midterm Multiple Choice Practice 1. Based on the construction below, which statement must be true? 1 1) m ABD m CBD 2 2) m ABD m CBD 3) m ABD m ABC 1 4) m CBD m ABD 2 2. Line segment AB is shown in the
Using inductive reasoning and conjectures Student Activity Sheet 2; use with Exploring The language of geometry
1. REINFORCE Find a geometric representation for the following sequence of numbers. 3, 4, 5, 6, 7, 2. What are the three undefined terms in geometry? 3. Write a description of a point. How are points labeled?
Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines
Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Two lines are if they are coplanar and do not intersect. Skew lines. Two
Which table shows the total cost for the given number of switches ordered?
lgebra 1 Review 1 Name: ate: 1 Find the missing term.?, 48, 12, 3 288 192 336 240 2 What are the next two terms in the pattern? 3,125, 625, 125, 25,... 30, 2 5, 1 30, 1 10, 2 opyright Pearson Education,
CHAPTER 3. Parallel & Perpendicular lines
CHAPTER 3 Parallel & Perpendicular lines 3.1- Identify Pairs of Lines and Angles Parallel Lines: two lines are parallel if they do not intersect and are coplaner Skew lines: Two lines are skew if they
Learn to use translations, reflections, and rotations to transform geometric shapes.
Learn to use translations, reflections, and rotations to transform geometric shapes. Insert Lesson Title Here Vocabulary transformation translation rotation reflection line of reflection A rigid transformation
HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934)
HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.1a
16.1 Segment Length and Midpoints
Name lass ate 16.1 Segment Length and Midpoints Essential Question: How do you draw a segment and measure its length? Explore Exploring asic Geometric Terms In geometry, some of the names of figures and
Semester 1 Final Exam Review
Target 1: Vocabulary and notation Semester 1 Final Exam Review Name 1. Find the intersection of MN and LO. 2. 3) Vocabulary: Define the following terms and draw a diagram to match: a) Point b) Line c)
Unit 6 Lesson 1 Circle Geometry Properties Project
Unit 6 Lesson 1 Circle Geometry Properties Project Name Part A Look up and define the following vocabulary words. Use an illustration where appropriate. Some of this vocabulary can be found in the glossary
Indicate whether the statement is true or false.
MATH 121 SPRING 2017 - PRACTICE FINAL EXAM Indicate whether the statement is true or false. 1. Given that point P is the midpoint of both and, it follows that. 2. If, then. 3. In a circle (or congruent
Geometry. ELG HS.G.14: Visualize relationships between two-dimensional and three-dimensional objects.
Vertical Progression: 7 th Grade 8 th Grade Geometry 7.G.A Draw, construct, and describe geometrical figures and describe the relationships between them. o 7.G.A.3 Describe the two-dimensional figures
Circles Assignment Answer the following questions.
Answer the following questions. 1. Define constructions. 2. What are the basic tools that are used to draw geometric constructions? 3. What is the use of constructions? 4. What is Compass? 5. What is Straight
Module Guidance Document. Geometry Module 2
Geometry Module 2 Topic A Scale Drawings 5 days Topic B Dilations 5 days Topic C Similarity and Dilations 15 days Topic D Applying Similarity to Right 7 days Triangles Topic D Trigonometry 13 days Just
Lesson 10.1 Skills Practice
Lesson 10.1 Skills Practice Location, Location, Location! Line Relationships Vocabulary Write the term or terms from the box that best complete each statement. intersecting lines perpendicular lines parallel
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 17, :30 to 3:30 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 17, 2017 12:30 to 3:30 p.m., only Student Name: School Name: The possession or use of any communications
3.3. You wouldn t think that grasshoppers could be dangerous. But they can damage
Grasshoppers Everywhere! Area and Perimeter of Parallelograms on the Coordinate Plane. LEARNING GOALS In this lesson, you will: Determine the perimeter of parallelograms on a coordinate plane. Determine
Parallel Lines Chapter Problems
Parallel Lines Chapter Problems Lines: Intersecting, parallel & skew Class Work Use image 1 1. Name all segments parallel to GH : 2. Name all segments skew to GH : 3. Name all segments intersecting with
University of Houston High School Mathematics Contest Geometry Exam Spring 2016
University of Houston High School Mathematics ontest Geometry Exam Spring 016 nswer the following. Note that diagrams may not be drawn to scale. 1. In the figure below, E, =, = 4 and E = 0. Find the length
Geometry Ch 3 Vertical Angles, Linear Pairs, Perpendicular/Parallel Lines 29 Nov 2017
3.1 Number Operations and Equality Algebraic Postulates of Equality: Reflexive Property: a=a (Any number is equal to itself.) Substitution Property: If a=b, then a can be substituted for b in any expression.
6.1B Lesson: Building Triangles Given Three Measurements*
6.1 Lesson: uilding Triangles Given Three Measurements* Name: Period: 1. ircle all the triangles with side lengths 8 and 5 and an included angle of 32. a. b. c. 2. ircle all the triangles with side lengths
6.1 Ratios, Proportions, and the Geometric Mean
6.1 Ratios, Proportions, and the Geometric Mean VOCABULARY Ratio of a to b Proportion Means and Extremes Geometric Mean EX1: Simplify Ratios Simplify the ratio. (See Table of Measures, p. 921) a. 76 cm:
Problem Solving with the Coordinate Plane
Grade 5 Module 6 Problem Solving with the Coordinate Plane OVERVIEW In this 40-day module, students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems.
Chapter 3, Part 1: Intro to the Trigonometric Functions
Haberman MTH 11 Section I: The Trigonometric Functions Chapter 3, Part 1: Intro to the Trigonometric Functions In Example 4 in Section I: Chapter, we observed that a circle rotating about its center (i.e.,
Geometry Station Activities for Common Core State Standards
Geometry Station Activities for Common Core State Standards WALCH EDUCATION Table of Contents Standards Correlations...................................................... v Introduction..............................................................vii
9.5 Properties and Conditions for Kites and Trapezoids
Name lass ate 9.5 Properties and onditions for Kites and Trapezoids ssential uestion: What are the properties of kites and trapezoids? Resource Locker xplore xploring Properties of Kites kite is a quadrilateral
Table of Contents. Standards Correlations...v Introduction...vii Materials List... x
Table of Contents Standards Correlations...v Introduction...vii Materials List... x...1...1 Set 2: Classifying Triangles and Angle Theorems... 13 Set 3: Corresponding Parts, Transformations, and Proof...
2.1 inductive reasoning and conjecture ink.notebook. September 07, Page 55. Ch 2. Reasoning. Page 56. and Proofs. 2.1 Inductive.
2.1 inductive reasoning and conjecture ink.notebook Page 55 Ch 2 Reasoning and Proofs Page 56 2.1 Inductive Reasoning Lesson Objectives Page 57 Standards Lesson Notes Page 58 2.1 Inductive Reasoning and
Lesson 4: General Pyramids and Cones and Their Cross-Sections
: General Pyramids and Cones and Their Cross-Sections Learning Target 1. I can state the definition of a general pyramid and cone, and that their respective cross-sections are similar to the base. 2. I
Name Date Class Period. 5.2 Exploring Properties of Perpendicular Bisectors
Name Date Class Period Activity B 5.2 Exploring Properties of Perpendicular Bisectors MATERIALS QUESTION EXPLORE 1 geometry drawing software If a point is on the perpendicular bisector of a segment, is
Downloaded from
1 IX Mathematics Chapter 8: Quadrilaterals Chapter Notes Top Definitions 1. A quadrilateral is a closed figure obtained by joining four points (with no three points collinear) in an order. 2. A diagonal
8.2 Slippery Slopes. A Solidify Understanding Task
7 8.2 Slippery Slopes A Solidify Understanding Task CC BY https://flic.kr/p/kfus4x While working on Is It Right? in the previous module you looked at several examples that lead to the conclusion that the
Lesson 1: Investigating Properties of Dilations
Lesson 1: Investigating Properties of Dilations Common Core Georgia Performance Standards MCC9 12.G.SRT.1a MCC9 12.G.SRT.1b Essential Questions 1. How are the preimage and image similar in dilations? 2.
Table of Contents Problem Solving with the Coordinate Plane
GRADE 5 UNIT 6 Table of Contents Problem Solving with the Coordinate Plane Lessons Topic 1: Coordinate Systems 1-6 Lesson 1: Construct a coordinate system on a line. Lesson 2: Construct a coordinate system
CONSTRUCTION #1: Segment Copy
CONSTRUCTION #1: Segment Copy Objective: Given a line segment, construct a line segment congruent to the given one. Procedure: After doing this Your work should look like this Start with a line segment
The Basics: Geometric Structure
Trinity University Digital Commons @ Trinity Understanding by Design: Complete Collection Understanding by Design Summer 6-2015 The Basics: Geometric Structure Danielle Kendrick Trinity University Follow
3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm.
1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School
AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School Copyright 2008 Pearson Education, Inc. or its affiliate(s). All rights reserved AGS Math Algebra 2 Grade
Find the coordinates of the midpoint of a segment having the given endpoints.
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to
S. Stirling Page 1 of 14
3.1 Duplicating Segments and ngles [and riangles] hese notes replace pages 144 146 in the book. You can read these pages for extra clarifications. Instructions for making geometric figures: You can sketch
2.1 Slope and Parallel Lines
Name Class ate.1 Slope and Parallel Lines Essential Question: How can ou use slope to solve problems involving parallel lines? Eplore Proving the Slope Criteria for Parallel Lines Resource Locker The following
B. Examples: 1. At NVHS, there are 104 teachers and 2204 students. What is the approximate teacher to student ratio?
Name Date Period Notes Formal Geometry Chapter 7 Similar Polygons 7.1 Ratios and Proportions A. Definitions: 1. Ratio: 2. Proportion: 3. Cross Products Property: 4. Equivalent Proportions: B. Examples:
TERRA Environmental Research Institute
TERRA Environmental Research Institute MATHEMATICS FCAT PRACTICE STRAND 3 Geometry and Spatial Sense Angle Relationships Lines and Transversals Plane Figures The Pythagorean Theorem The Coordinate Plane
*Unit 1 Constructions and Transformations
*Unit 1 Constructions and Transformations Content Area: Mathematics Course(s): Geometry CP, Geometry Honors Time Period: September Length: 10 blocks Status: Published Transfer Skills Previous coursework:
Angles formed by Transversals
Section 3-1: Parallel Lines and Transversals SOL: None Objectives: Identify the relationships between two lines or two planes Name angles formed by a pair of lines and a transversal Vocabulary: Parallel
Project Maths Geometry Notes
The areas that you need to study are: Project Maths Geometry Notes (i) Geometry Terms: (ii) Theorems: (iii) Constructions: (iv) Enlargements: Axiom, theorem, proof, corollary, converse, implies The exam
Perry High School. Geometry: Week 3
Geometry: Week 3 Monday: Labor Day! Tuesday: 1.5 Segments and Angle Bisectors Wednesday: 1.5 - Work Thursday: 1.6 Angle Pair Relationships Friday: 1.6-Work Next Week 1.7, Review, Exam 1 on FRIDAY 1 Tuesday:
Investigation and Exploration Dynamic Geometry Software
Investigation and Exploration Dynamic Geometry Software What is Mathematics Investigation? A complete mathematical investigation requires at least three steps: finding a pattern or other conjecture; seeking
Building Blocks of Geometry
Practice A Building Blocks of Geometry Write the following in geometric notation. 1. line EF 2. ray RS 3. line segment JK Choose the letter for the best answer. 4. Identify a line. A BD B AD C CB D BD
G-SRT Dilating a Line
G-SRT Dilating a Line Alignments to Content Standards: G-SRT.A.1.b G-SRT.A.1.a G-SRT.A.1 Task Suppose we apply a dilation by a factor of 2, centered at the point P, to the figure below. a. In the picture,
Unit 1 NOTES Honors Math 2 18
Unit 1 NOTES Honors Math 2 18 Day 5: Copositions War-Up: Given triangle GHI with G(-2, 1), H(3, 4), and I(1, 5), find the points of the iage under the following transforations and write the lgebraic Rule.
1. What are the coordinates for the viewer s eye?
Part I In this portion of the assignment, you are going to draw the same cube in different positions, using the Perspective Theorem. You will then use these pictures to make observations that should reinforce
JMG. Review Module 1 Lessons 1-20 for Mid-Module. Prepare for Endof-Unit Assessment. Assessment. Module 1. End-of-Unit Assessment.
Lesson Plans Lesson Plan WEEK 161 December 5- December 9 Subject to change 2016-2017 Mrs. Whitman 1 st 2 nd Period 3 rd Period 4 th Period 5 th Period 6 th Period H S Mathematics Period Prep Geometry Math
Tangents to Circles. The distance across the circle, through its center, is the diameter of the circle. The diameter is twice the radius.
ircles Tangents to ircles circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. circle with center P is called circle P. The distance from
The Formal Proof of a Theorem
.7 The Formal Proof of a Theorem 5.7 The Formal Proof of a Theorem KY ONPTS Formal Proof of a Theorem onverse of a Theorem Picture Proof (Informal) of a Theorem Recall from Section. that statements that
Geometry Midterm Review Spring 2011 Name Date Period. 2. Name three points that are collinear Name a pair of opposite rays. 3.
Name Date Period Unit 1 1. Give two other names for AB. 1. 2. Name three points that are collinear. 2. 3. Name a pair of opposite rays. 3. 4. Give another name for CD. 4. Point J is between H and K on
Worksheet 10 Memorandum: Construction of Geometric Figures. Grade 9 Mathematics
Worksheet 10 Memorandum: Construction of Geometric Figures Grade 9 Mathematics For each of the answers below, we give the steps to complete the task given. We ve used the following resources if you would
Georgia Department of Education Common Core Georgia Performance Standards Framework Analytic Geometry Unit 1
Lunch Lines Mathematical Goals Prove vertical angles are congruent. Understand when a transversal is drawn through parallel lines, special angles relationships occur. Prove when a transversal crosses parallel
0810ge. Geometry Regents Exam y # (x $ 3) 2 % 4 y # 2x $ 5 1) (0,%4) 2) (%4,0) 3) (%4,%3) and (0,5) 4) (%3,%4) and (5,0)
0810ge 1 In the diagram below, ABC! XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements
Problem of the Month: Between the Lines
Problem of the Month: Between the Lines Overview: In the Problem of the Month Between the Lines, students use polygons to solve problems involving area. The mathematical topics that underlie this POM are
L7 Constructions 7.1 Construction Introduction Per Date
7.1 Construction Introduction Per Date In pairs, discuss the meanings of the following vocabulary terms. The first two you should attempt to recall from memory, and for the rest you should try to agree
Geometry - Midterm Exam Review - Chapters 1, 2
Geometry - Midterm Exam Review - Chapters 1, 2 1. Name three points in the diagram that are not collinear. 2. Describe what the notation stands for. Illustrate with a sketch. 3. Draw four points, A, B,
Georgia Department of Education Common Core Georgia Performance Standards Framework Student Edition Analytic Geometry Unit 1
Analytic Geometry Unit 1 Lunch Lines Mathematical goals Prove vertical angles are congruent. Understand when a transversal is drawn through parallel lines, special angles relationships occur. Prove when
9.5 symmetry 2017 ink.notebook. October 25, Page Symmetry Page 134. Standards. Page Symmetry. Lesson Objectives.
9.5 symmetry 2017 ink.notebook Page 133 9.5 Symmetry Page 134 Lesson Objectives Standards Lesson Notes Page 135 9.5 Symmetry Press the tabs to view details. 1 Lesson Objectives Press the tabs to view details.
Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6
DOE Assessment Guide Questions (2015) Analytic Geometry EOC Study Booklet Geometry Domain Units 1-3 & 6 Question Example Item #1 Which transformation of ΔMNO results in a congruent triangle? Answer Example
Rational Points On Elliptic Curves - Solutions. (i) Throughout, we ve been looking at elliptic curves in the general form. y 2 = x 3 + Ax + B
Rational Points On Elliptic Curves - Solutions (Send corrections to cbruni@uwaterloo.ca) (i) Throughout, we ve been looking at elliptic curves in the general form y 2 = x 3 + Ax + B However we did claim
Math 7 Notes - Unit 08B (Chapter 5B) Proportions in Geometry
Math 7 Notes - Unit 8B (Chapter B) Proportions in Geometr Sllabus Objective: (6.23) The student will use the coordinate plane to represent slope, midpoint and distance. Nevada State Standards (NSS) limits
Plot the points. Then connect the vertices, X', Y', and Z' to form the reflected image.
Graph each figure and its image under the given reflection. 11. rectangle ABCD with A(2, 4), B(4, 6), C(7, 3), and D(5, 1) in the x-axis. To reflect over the x-axis, multiply the y-coordinate of each vertex
Basic Geometry. Editors: Mary Dieterich and Sarah M. Anderson Proofreader: Margaret Brown. COPYRIGHT 2011 Mark Twain Media, Inc.
asic Geometry Editors: Mary Dieterich and Sarah M. nderson Proofreader: Margaret rown COPYRIGHT 2011 Mark Twain Media, Inc. ISN 978-1-58037-999-1 Printing No. 404154-E Mark Twain Media, Inc., Publishers
Geometer s Skethchpad 8th Grade Guide to Learning Geometry
Geometer s Skethchpad 8th Grade Guide to Learning Geometry This Guide Belongs to: Date: Table of Contents Using Sketchpad - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Lesson 9.1 Assignment
Lesson 9.1 Assignment Name Date Earth Measure Introduction to Geometry and Geometric Constructions Use a compass and a straightedge to complete Questions 1 and 2. 1. Construct a flower with 12 petals by
1 Version 2.0. Related Below-Grade and Above-Grade Standards for Purposes of Planning for Vertical Scaling:
Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Content Domain: Geometry Target E [a]: Draw, construct,
Chapter 11: Constructions and Loci
Chapter 11: Section 11.1a Constructing a Triangle given 3 sides (sss) Leave enough room above the line to complete the shape. Do not rub out your construction lines. They show your method. 1 Section 11.1b
9.1 Properties of Parallelograms
Name lass ate 9.1 Properties of Parallelograms Essential Question: What can you conclude about the sides, angles, and diagonals of a parallelogram? Explore Investigating Parallelograms quadrilateral is
JK XY LJ LJ ZX KL KL YZ LJ KL YX KJ. Final Exam Review Modules 10 16, 18 19
Geometry Final Exam Review Modules 10 16, 18 19 Use the following information for 1 3. The figure is symmetric about the x axis. Name: 6. In this figure ~. Which statement is not true? A JK XY LJ ZX C