Rigid Motion vs. Non-rigid Motion Transformations
|
|
|
- Mildred Thompson
- 5 years ago
- Views:
Transcription
1 Rigid Motion vs. Non-rigid Motion Transformations What are some things you think of when we say going to a theme park. Have you ever been to a theme park? If so, when and where was it? What was your best memory about the theme park? If not, where would be the first theme park you would like to go to and why? Rigid Motion Transformations: A transformation of points in space consisting of a sequence of one or more translations, reflections, and/or rotations. Rigid motions preserve distances and angle measures. Referring to the virtual Theme Park: Describe the object, identify the transformation, describe the transformation and state if it is a rigid motion transformation or not. Object 1: Object 2: Object 3: Object 4: Rigid vs. Non-Rigid Transformations 1
2 1. Use the rule at the top of each column to find the coordinates of each new image. Plot each new triangle on the graph. (x,y) (2x,2y) (3x,3y) (4x,4y) (5x,5y) A(1,2) A (, ) A (, ) A (, ) A (, ) B(3,1) B (, ) B (, ) B (, ) B (, ) C(3, 3) C (, ) C (, ) C (, ) C (, ) 2. Explain what happened to Triangle ABC. 3. How much larger is the length of A B than the length of AB? 4. How much larger is the length of A B than the length of AB? 5. How much larger is the length of A B than the length of AB? 6. Verify your answers to questions 3 5 using a compass. Rigid vs. Non-Rigid Transformations 2
3 7. Find the slopes of each of the following segments. a) AB b) A B c) A B d) A B e) A B 8. What conclusion can you draw from your answers to question 7? 9. Draw a line through all the A s, then another line through all the B s and then another line through all the C s. Make sure your line extends across the entire coordinate plane. What do you notice? The point where all the lines intersect is called the center of dilation. The center of dilation is a fixed point in the plane about which all points are expanded or contracted. Label the center of dilation X. 10. How much larger is the length of A X than the length of AX? 11. How much larger is the length of A X than the length of AX? 12. How much larger is the length of A X than the length of AX? 13. Verify your answers to questions using a compass. Definition of Dilation: Dilation is a transformation that moves each point along a ray through the point originating from a fixed center and multiplies distances from the center by a common scale factor; where a figure is made proportionally larger or smaller. 14. Are dilations rigid motions transformations? Explain. Rigid vs. Non-Rigid Transformations 3
4 Constructing Dilations (when center of dilation is outside a figure) 1. Point C is the center of dilation. Follow the following steps to dilate the triangle. Step 1: Draw rays CX, CY, and CZ. Step 2: With your compass, measure the CX. Transfer this distance along CX so that you find point X such that CX = 2(CX). Step 3: Repeat Step 2 with Points Y and Z. Rigid vs. Non-Rigid Transformations 4
5 Constructing Dilations (when center of dilation is on a figure) 2. Point C is the center of dilation. Follow the following steps to dilate the triangle. Step 1: Draw rays CX, CY, and CZ. Step 2: With your compass, measure the CX. Transfer this distance along CX so that you find point X such that CX = 3(CX). Step 3: Repeat Step 2 with Points Y and Z. Rigid vs. Non-Rigid Transformations 5
6 Constructing Dilations (when center of dilation is inside a figure) 3. Point C is the center of dilation. Follow the following steps to dilate the triangle. Step 1: Draw rays CX, CY, and CZ. Step 2: With your compass, measure the CX. Transfer this distance along CX so that you find point X such that CX = 2(CX). Step 3: Repeat Step 2 with Points Y and Z. Rigid vs. Non-Rigid Transformations 6
7 Materials: Teacher Directions Handouts 1 per student Straightedge Compass Computer/Overhead projector and (Geogebra Installed or internet access) Objective: Students will determine the difference between rigid and non-rigid transformations. Directions: Begin class by having students complete the introduction regarding theme parks. Show the geogebra applet after a few students have shared their responses about theme parks. If you have geogebra installed on your computer open file: Rigid vs Non Rigid Intro.ggb If you have internet access go to: Have a student read the definition of rigid motion transformation then describe object 1, object 2, object 3, object 4. Share answers and let students know that we will focus on non-rigid motion transformations today. Problems 1 5. Students should be able to complete Problems 1 5 on their own. (10 mins) Call on students to share answers to questions 3,4, and 5. Before continuing on in the lesson, demonstrate to students how they can use a compass to measure and compare lengths. Demonstrate how to copy a segment on the board. Then have students complete problem 6, and verify their answers to 5. Problems 6 13 Students should be able to complete 6 13 on their own. (15 minutes) Call on students to share their response to problem 8. Have a discussion around the relationship between corresponding segments of dilated figures. Corresponding segments are // to each other and there exists a scale factor that relates the lengths of the corresponding segments. Rigid vs. Non-Rigid Transformations 7
8 Call on students to share their response to problem 9. Have discussion around the center of dilation. Ask students, What would happen we moved the triangle so the center of dilation was inside of the triangle and did the problem again? What will our picture look like then? Think-Pair-Share Have a student read the definition of dilation out loud. Compare definition to our picture that students created. Ask what do we call the fixed center? What were the scale factors that we used in these problems? What scale factors would reduce or shrink our figure? Have students complete problem 15 and share answers aloud. Tell students that this unit will focus only on rigid motion transformations so we will not cover dilations again till later on. Our focus will be on transformations that preserve congruence: translations, reflections, and rotations. Have students complete the constructions on their own. Give students a few minutes to struggle with the directions for the constructions before modeling how to do the problem. Extension: You can have students write relationships between pre-image and image segments in regards to length and direction. Rigid vs. Non-Rigid Transformations 8
Transformations & Basic Geometry Vocabulary
Transformations & Basic Geometry Vocabulary Key Terms and Concepts Name: Date: Period: Rigid Transformations Toolkit Key Vocabulary- Give a precise definition of each term Parallel lines: Perpendicular
Guided Problem Solving
-1 Guided Problem Solving GPS Student Page 57, Exercises 1 1: Match each rule with the correct translation. A. (x, y) (x, y 1 ) I. P(, 1) P (3, ) B. (x, y) (x 1 3, y) II. Q(3, 0) Q (3, ) C. (x, y) (x 1,
8.2.1 and 2 Lesson Date: Definition of Translation and Three Basic Properties
8.2.1 and 2 Lesson Date: Definition of Translation and Three Basic Properties Student Objectives I can perform translations of figures along a specific vector. I can label the image of the figure using
5.2. In mathematics, when a geometric figure is transformed, the size and shape of the. Hey, Haven t I Seen You Before? Congruent Triangles
Hey, Haven t I Seen You Before? Congruent Triangles. Learning Goals In this lesson, you will: Identify corresponding sides and corresponding angles of congruent triangles. Explore the relationship between
DO NOW Geometry Regents Lomac Date. due. Similar by Transformation Construction
DO NOW Geometry Regents Lomac 2014-2015 Date. due. Similar by Transformation Construction (DN) What defines a similarity transformation? Name Per LO: I can construct a similarity transformation. (1) compass,
4-1 Congruence and Transformations
4-1 Congruence and Transformations Warm Up Lesson Presentation Lesson Quiz Holt Geometry McDougal Geometry Objectives Draw, identify, and describe transformations in the coordinate plane. Use properties
Translations SLIDE. Example: If you want to move a figure 5 units to the left and 3 units up we would say (x, y) (x-5, y+3).
Translations SLIDE Every point in the shape must move In the same direction The same distance Example: If you want to move a figure 5 units to the left and 3 units up we would say (x, y) (x-5, y+3). Note:
Math 8 Module 3 End of Module Study Guide
Name ANSWER KEY Date 3/21/14 Lesson 8: Similarity 1. In the picture below, we have a triangle DEF that has been dilated from center O, by scale factor r = ½. The dilated triangle is noted by D E F. We
Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr.
Common Core Standard: 8.G.3 Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 6.2.1 What
6.2 Triangle Dilations A Solidify Understanding Task
6.2 Triangle Dilations A Solidify Understanding Task 1. Given ABC, use point M as the center of a dilation to locate the vertices of a triangle that has side lengths that are three times longer than the
Lesson 1. Unit 2 Practice Problems. Problem 2. Problem 1. Solution 1, 4, 5. Solution. Problem 3
Unit 2 Practice Problems Lesson 1 Problem 1 Rectangle measures 12 cm by 3 cm. Rectangle is a scaled copy of Rectangle. Select all of the measurement pairs that could be the dimensions of Rectangle. 1.
Chapter 12 Transformations: Shapes in Motion
Chapter 12 Transformations: Shapes in Motion 1 Table of Contents Reflections Day 1.... Pages 1-10 SWBAT: Graph Reflections in the Coordinate Plane HW: Pages #11-15 Translations Day 2....... Pages 16-21
12.4 Rotations. Learning Objectives. Review Queue. Defining Rotations Rotations
12.4. Rotations www.ck12.org 12.4 Rotations Learning Objectives Find the image of a figure in a rotation in a coordinate plane. Recognize that a rotation is an isometry. Review Queue 1. Reflect XY Z with
Unit 1 NOTES Honors Math 2 1
Unit 1 NOTES Honors Math 2 1 Day 1: Introduction to Transformations and Translations Warm-Up: Prerequisite Skill: Graphing Lines Graph the following lines. 1) x = 2 2) y = 4 3) y = x (Hint: this is y =
B ABC is mapped into A'B'C'
h. 00 Transformations Sec. 1 Mappings & ongruence Mappings Moving a figure around a plane is called mapping. In the figure below, was moved (mapped) to a new position in the plane and the new triangle
Wednesday, November 7, 2018
Wednesday, November 7, 2018 Warm-up Use the grid from yesterday s warm-up space to plot the pre-image ABCD and the points that are transformed by the rule (x, y) (2x, 2y) 5 2 2 5 2 4 0 0 Talk about quiz
Lesson 5: Definition of Rotation and Basic Properties
Student Outcomes Students know how to rotate a figure a given degree around a given center. Students know that rotations move lines to lines, rays to rays, segments to segments, and angles to angles. Students
Course Guide (/8/teachers/teacher_course_guide.html) Print (/8/teachers/print_materials.html) LMS (/8
(http://openupresources.org)menu Close OUR Curriculum (http://openupresources.org) Professional Development (http://openupresources.org/illustrative-mathematics-professional-development) Implementation
Geometry: Unit 1: Transformations. Chapter 14 (In Textbook)
Geometry: Unit 1: Transformations Chapter 14 (In Textbook) Transformations Objective: Students will be able to do the following, regarding geometric transformations. Write Transformations Symbolically
Name: Date: Per: WARM UP
Name: Date: Per: 6.1.1-6.1.3 WARM UP 6-23. In the last three lessons, you have investigated rigid transformations: reflections, rotations, and translations. 1. What happens to a shape when you perform
2-1 Transformations and Rigid Motions. ENGAGE 1 ~ Introducing Transformations REFLECT
2-1 Transformations and Rigid Motions Essential question: How do you identify transformations that are rigid motions? ENGAGE 1 ~ Introducing Transformations A transformation is a function that changes
CCM6+/7+ - Unit 13 - Page 1 UNIT 13. Transformations CCM6+/7+ Name: Math Teacher: Projected Test Date:
CCM6+/7+ - Unit 13 - Page 1 UNIT 13 Transformations CCM6+/7+ Name: Math Teacher: Projected Test Date: Main Idea Pages Unit 9 Vocabulary 2 Translations 3 10 Rotations 11 17 Reflections 18 22 Transformations
B ABC is mapped into A'B'C'
h. 00 Transformations Sec. 1 Mappings & ongruence Mappings Moving a figure around a plane is called mapping. In the figure below, was moved (mapped) to a new position in the plane and the new triangle
UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 6: Defining and Applying Similarity Instruction
Prerequisite Skills This lesson requires the use of the following skills: creating ratios solving proportions identifying congruent triangles calculating the lengths of triangle sides using the distance
B ABC is mapped into A'B'C'
h. 00 Transformations Sec. 1 Mappings & ongruence Mappings Moving a figure around a plane is called mapping. In the figure below, was moved (mapped) to a new position in the plane and the new triangle
Vocabulary for Student Discourse Pre-image Image Reflect Symmetry Transformation Rigid transformation Congruent Mapping Line of symmetry
Lesson 3 - page 1 Title: Reflections and Symmetry I. Before Engagement Duration: 2 days Knowledge & Skills Understand transformations as operations that map a figure onto an image Understand characteristics
Isometries: Teacher Notes
Isometries: Teacher Notes Henri Picciotto Acknowledgments Vinci Daro, Ann Shannon, and Celia Stevenson helped me with the original version of this document. Zalman Usiskin offered valuable feedback, some
Size Transformations in the Coordinate Plane
Size Transformations in the Coordinate Plane I.e. Dilations (adapted from Core Plus Math, Course 2) Concepts 21-26 Lesson Objectives In this investigation you will use coordinate methods to discover several
Lesson Plan #41. Class: Geometry Date: Monday December 17 th, 2018
Lesson Plan #41 Class: Geometry Date: Monday December 17 th, 2018 Topic: Rotations Objectives: 1) Students will be review line and point symmetry. 2) Students will be able to define a rotation. 3) Students
Chapter 2: Transformations. Chapter 2 Transformations Page 1
Chapter 2: Transformations Chapter 2 Transformations Page 1 Unit 2: Vocabulary 1) transformation 2) pre-image 3) image 4) map(ping) 5) rigid motion (isometry) 6) orientation 7) line reflection 8) line
Input/Output Machines
UNIT 1 1 STUDENT BOOK / Machines LESSON Quick Review t Home c h o o l This is an / machine It can be used to make a growing pattern Each input is multiplied by 9 to get the output If you input 1, the output
Name: Geometry Practice Test Unit 2 Transformations in the Plane. Date: Pd:
Geometry Practice Test Unit 2 Transformations in the Plane (G.CO.A.2 - G.CO.A.5) Name: Date: Pd: 1) What type of symmetry is shown in this picture? (multiple choices-select all that apply) A) Point symmetry
Reflections, Translations, and Dilations
Reflections, Translations, and Dilations Step 1: Graph and label the following points on your coordinate plane. A (2,2) B (2,8) C (8,8) D (8,2) Step 2: Step 3: Connect the dots in alphabetical order to
Lesson 11.1 Dilations
Lesson 11.1 Dilations Key concepts: Scale Factor Center of Dilation Similarity A A dilation changes the size of a figure. B C Pre Image: 1 A A' B C Pre Image: B' C' Image: What does a dilation NOT change?
Construction Blueprints A Practice Understanding Task
90 Construction Blueprints A Practice Understanding Task For each of the following straightedge and compass constructions, illustrate or list the steps for completing the construction and give an eplanation
AA~ is/is not sufficient to guarantee that two triangles are similar.
DO NOW Geometry Regents Lomac 2014-2015 Date. due. Similar Triangles Shortcuts AA, SSS, SAS 6.3 (DN) ON THE BACK OF THIS PACKET What defines a similarity transformation? Name Per LO: I can show that triangles
L11 Dilations and Similarity 11.1 Ratio Review Warmup Per Date. 1. Fill in the table below as demonstrated in the sample top row.
11.1 Ratio Review Warmup Per Date 1. Fill in the table below as demonstrated in the sample top row. Ratio Fraction Equation Written x to y is 3 x y =3 x = 3y x is 3 times as big as y x to y is ½ x y =2
TRANSFORMATIONS AND CONGRUENCE
21 TRANSFORMATIONS AND CONGRUENCE INSTRUCTIONAL ACTIVITY Lesson 3 LEARNING GOAL Students will discover the impact of translations and reflections on the coordinates of a figure, then generalize the rule
G-SRT Similar triangles
G-SRT Similar triangles Alignments to Content Standards: G-SRT.A.3 Task In the two triangles pictured below m( A) = m( D) and m( B) = m( E) : 1 Using a sequence of translations, rotations, reflections,
Math Geometry FAIM 2015 Form 1-A [ ]
![Math Geometry FAIM 2015 Form 1-A [ ]](/thumbs/80/81205175.jpg "Math Geometry FAIM 2015 Form 1-A [ ]")
Math Geometry FAIM 2015 Form 1-A [1530458] Student Class Date Instructions Use your Response Document to answer question 13. 1. Given: Trapezoid EFGH with vertices as shown in the diagram below. Trapezoid
Date Target Assignment Done! 2.1 Quiz 2.2 Quiz 2.3 Quiz Unit 2 Test
Name Unit 2 Transformations Target 1: Identify and determine congruent parts given a rigid motion. Target 2: Perform and identify rigid transformations of points, segments, and figures. a. Perform and
Learning Log Title: CHAPTER 6: TRANSFORMATIONS AND SIMILARITY. Date: Lesson: Chapter 6: Transformations and Similarity
Chapter 6: Transformations and Similarity CHAPTER 6: TRANSFORMATIONS AND SIMILARITY Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 6: Transformations and Similarity Date: Lesson:
Module 1 Topic C Lesson 14 Reflections
Geometry Module 1 Topic C Lesson 14 Reflections The purpose of lesson 14 is for students to identify the properties of reflection, to use constructions to find line of reflection, get familiar with notations
Construction Blueprints A Practice Understanding Task
90 Construction Blueprints A Practice Understanding Task For each of the following straightedge and compass constructions, illustrate or list the steps for completing the construction and give an eplanation
DE to a line parallel to Therefore
Some Proofs 1. In the figure below segment DE cuts across triangle ABC, and CD/CA = CE/CB. Prove that DE is parallel to AB. Consider the dilation with center C and scaling factor CA/CD. This dilation fixes
Unit 4 Guided Notes Part 2 Geometry
Unit 4 Guided Notes Part 2 Geometry Name: Important Vocabulary: Transformation: A change in,, or of a geometric figure. Rigid transformation: A transformation that preserves measures and of segments. Transformation
I can identify reflections, rotations, and translations. I can graph transformations in the coordinate plane.
Page! 1 of! 14 Attendance Problems. 1. Sketch a right angle and its angle bisector. 2. Draw three different squares with (3, 2) as one vertex. 3. Find the values of x and y if (3, 2) = (x + 1, y 3) Vocabulary
Students are not expected to work formally with properties of dilations until high school.
Domain: Geometry (G) Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software. Standard: 8.G.1. Verify experimentally the properties of rotations, reflections,
Lesson 22: Congruence Criteria for Triangles SAS
Student Outcomes Students learn why any two triangles that satisfy the SAS congruence criterion must be congruent. Lesson Notes In, we begin to investigate criteria, or the indicators, of triangle congruence.
Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1
Name Date Student Guide Lesson 3: Triangle Congruence: SSS, SAS, and ASA, Part 1 Bridges, ladders, containers, and other items that need to be sturdy often use triangles. A combination of triangles is
G.CO.A.2: Identifying Transformations 2
G.CO.A.2: Identifying Transformations 2 1 In the accompanying diagram, ABC is similar to but not congruent to A B C. 3 In the diagram below, A' B' is the image of AB under which single transformation?
Unit 7. Transformations
Unit 7 Transformations 1 A transformation moves or changes a figure in some way to produce a new figure called an. Another name for the original figure is the. Recall that a translation moves every point
7. 2 More Things Under. Construction. A Develop Understanding Task
7 Construction A Develop Understanding Task Like a rhombus, an equilateral triangle has three congruent sides. Show and describe how you might locate the third vertex point on an equilateral triangle,
2D Shapes, Scaling, and Tessellations
2D Shapes, Scaling, and Tessellations Name(s): Sarah Hunter Title of lesson: How do different shapes fit together? Date of lesson: Week 2, Day 5 Length of lesson: 50 Minutes (1 Class Period) Description
Isometries of the Plane Teacher s Notes
Isometries of the Plane Teacher s Notes Henri Picciotto This unit is intended to be consistent with the Common Core State Standards for Mathematics (CCSSM), but it does go quite a bit further than is required
9 Transformations CHAPTER. Chapter Outline.
Chapter 9 www.ck12.org CHAPTER 9 Transformations Chapter Outline 9.1 EXPLORING SYMMETRY 9.2 TRANSLATIONS AND VECTORS 9.3 REFLECTIONS 9.4 ROTATIONS 9.5 COMPOSITION OF TRANSFORMATIONS 9.6 DILATIONS 9.7 TESSELLATIONS
8.G Reflections, Rotations, and
8.G Reflections, Rotations, and Translations Alignments to Content Standards: 8.G.A.1 Task In this task, using computer software, you will apply reflections, rotations, and translations to a triangle.
8.G Triangle congruence with coordinates
8.G Triangle congruence with coordinates Alignments to Content Standards: 8.G.A.2 8.G.A.3 Task Triangles ABC and PQR are shown below in the coordinate plane: 1 ABC PQR a. Show that is congruent to with
Unit 14: Transformations (Geometry) Date Topic Page
Unit 14: Transformations (Geometry) Date Topic Page image pre-image transformation translation image pre-image reflection clockwise counterclockwise origin rotate 180 degrees rotate 270 degrees rotate
Lesson 9 Reflections Learning Targets :
Reflections Learning Targets : I can construct the line of reflection using the compass and a straightedge I can draw the reflected figure using a compass and a straightedge and on coordinate grid Opening
Geometry CP. Unit 1 Notes
Geometry CP Unit 1 Notes 1.1 The Building Blocks of Geometry The three most basic figures of geometry are: Points Shown as dots. No size. Named by capital letters. Are collinear if a single line can contain
Properties of Rotations
Properties of Rotations Student Probe Find the image of a 50 o counterclockwise rotation about point P. A P B Lesson Description The lesson examines rotations as the transformation obtained by reflecting
Ohio Tutorials are designed specifically for the Ohio Learning Standards to prepare students for the Ohio State Tests and end-ofcourse
Tutorial Outline Ohio Tutorials are designed specifically for the Ohio Learning Standards to prepare students for the Ohio State Tests and end-ofcourse exams. Math Tutorials offer targeted instruction,
Similar Polygons. These rectangles are not similar. In the investigation, you will explore what makes polygons similar.
CONDENSED LESSON 11.1 Similar Polygons In this lesson, you Learn what it means for two figures to be similar Use the definition of similarity to find missing measures in similar polygons Explore dilations
Study Guide - Geometry
Study Guide - Geometry (NOTE: This does not include every topic on the outline. Take other steps to review those.) Page 1: Rigid Motions Page 3: Constructions Page 12: Angle relationships Page 14: Angle
Construction: Draw a ray with its endpoint on the left. Label this point B.
Name: Ms. Ayinde Date: Geometry CC 1.13: Constructing Angles Objective: To copy angles and construct angle bisectors using a compass and straightedge. To construct an equilateral triangle. Copy an Angle:
Properties of Rotations
Properties of Rotations Student Probe Find the image of a 50 counterclockwise rotation about point P. Lesson Description The lesson examines rotations as the transformation obtained by reflecting an object
(3) Proportionality. The student applies mathematical process standards to use proportional relationships
Title: Dilation Investigation Subject: Coordinate Transformations in Geometry Objective: Given grid paper, a centimeter ruler, a protractor, and a sheet of patty paper the students will generate and apply
UNIT 5 GEOMETRY TEMPLATE CREATED BY REGION 1 ESA UNIT 5
UNIT 5 GEOMETRY TEMPLATE CREATED BY REGION 1 ESA UNIT 5 Geometry Unit 5 Overview: Circles With and Without Coordinates In this unit, students prove basic theorems about circles, with particular attention
9/20/2017 High School Geometry Common Core G.SRT.A.1 - Dilation Properties - Teacher Notes - Patterson
HOME Organize UNIT #1 UNIT #2 UNIT #3 UNIT #4 UNIT #5 UNIT #6 Resources Assessment Notes Teaching Items Teacher Notes CONCEPT 1 The properties and characteristics of dilations. Dilation is the term that
8.G Cutting a rectangle into two congruent triangles
8.G Cutting a rectangle into two congruent triangles Task ABCD AC Below is a picture of rectangle with diagonal. ACD 180 D A A C C a. Draw the image of triangle when it is rotated about vertex. Call the
PARCC Review 1. Select the drop-down menus to correctly complete each sentence.
Name PARCC Review 1. Select the drop-down menus to correctly complete each sentence. The set of all points in a plane that are equidistant from a given point is called a The given point is called the Radius
Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr.
Common Core Standard: 8.G.3, 8.G.4 Is there a different way to get the same result? Did we give enough information? How can we describe the position? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 6.2.2
Geometry Ch 1
Geometry Ch 1 http://mcsmgeometry.weebly.com Lesson 1 What are the three undefined terms in Geometry? (Section 1.1) HW #1: P5 8: 1, 5, 6, 8, 15, 19, 33, 35, 36 Objectives: name a segment, a line, a ray,
Chapter 1. Linear Equations and Straight Lines. 2 of 71. Copyright 2014, 2010, 2007 Pearson Education, Inc.
Chapter 1 Linear Equations and Straight Lines 2 of 71 Outline 1.1 Coordinate Systems and Graphs 1.4 The Slope of a Straight Line 1.3 The Intersection Point of a Pair of Lines 1.2 Linear Inequalities 1.5
Module 3: Similarity Topic B: Similar Figures. Lesson 3-10: Informal Proof of AA Criterion for Similarity
Module 3: Similarity Topic B: Similar Figures Lesson 3-10: Informal Proof of AA Criterion for Similarity Lesson 3-10: Informal Proof of AA Criterion for Similarity Purpose for Learning: EssenCal QuesCon(s):
JMG. Algebra II. Resigning from a job. Working with Radian Measures & the Unit Circle Students. How to Effectively Write a Letter of Resignation
Lesson Plans Lesson Plan WEEK 35 May 8-May 12 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 Extensions
UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 5: Congruent Triangles Instruction
Prerequisite Skills This lesson requires the use of the following skills: recognizing transformations performed as a combination of translations, reflections, rotations, dilations, contractions, or stretches
Similarity Review (Unit 4)
Similarity Review (Unit 4) Name Using a compass and straightedge construct the image of the figure after a dilation with point C as the center of dilation and the given scale factor. Label the vertices
Module 2 Test Study Guide. Type of Transformation (translation, reflection, rotation, or none-of-theabove). Be as specific as possible.
Module 2 Test Study Guide CONCEPTS TO KNOW: Transformation (types) Rigid v. Non-Rigid Motion Coordinate Notation Vector Terminology Pre-Image v. Image Vertex Prime Notation Equation of a Line Lines of
Instructional Focus: Use dilations to show figures similar.
Instructional Focus: Use dilations to show figures. Properties of Dilations (G.SRT.1) Suppose we apply a dilation by a factor of 2, centered at the point P to the figure. a. In the picture, locate the
a triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles
acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
Transformations. Lesson Summary: Students will explore rotations, translations, and reflections in a plane.
Transformations Lesson Summary: Students will explore rotations, translations, and reflections in a plane. Key Words: Transformation, translation, reflection, rotation Background knowledge: Students should
Geometry. Topic 1 Transformations and Congruence
Geometry Topic 1 Transformations and Congruence MAFS.912.G-CO.1.2 Consider the point A at ( 3, 5). A. Find the coordinates of A, the image of A after the transformation: (, ) (, ). B. What type of transformation
Geometry R. Unit 12 Coordinate Geometry. Day Classwork Day Homework Wednesday 3/7 Thursday 3/8 Friday 3/9
Geometry R Unit 12 Coordinate Geometry Day Classwork Day Homework Wednesday 3/7 Thursday 3/8 Friday 3/9 Unit 11 Test Review Equations of Lines 1 HW 12.1 Perimeter and Area of Triangles in the Coordinate
Unit 3: Congruence & Similarity
Approximate Time Frame: 6 weeks Connections to Previous Learning: In previous grades, students made scale drawings of geometric figures and solved problems involving angle measure, surface area, and volume.
Study Guide - Chapter 6
8 th Grade Name Date Period Study Guide - Chapter 6 1) Label each quadrant with I, II, III, or IV. 2) Use your knowledge of rotations to name the quadrant that each point below will land in after the rotation
Name: 1) Which of the following properties of an object are not preserved under a rotation? A) orientation B) none of these C) shape D) size
Name: 1) Which of the following properties of an object are not preserved under a rotation? A) orientation B) none of these C) shape D) size 2) Under a certain transformation, A B C is the image of ABC.
How do the shapes grow or shrink? What parts can we compare? How can we write the comparison? CPM Materials modified by Mr. Deyo
Common Core Standard: 8.G.2, 8.G.4 How do the shapes grow or shrink? What parts can we compare? How can we write the comparison? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 6.2.4 What Sequence Makes
UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS
UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS This unit introduces the concepts of similarity and congruence. The definition of similarity is explored through dilation transformations. The concept of scale
Ohio Tutorials are designed specifically for the Ohio Learning Standards to prepare students for the Ohio State Tests and end-ofcourse
Tutorial Outline Ohio Tutorials are designed specifically for the Ohio Learning Standards to prepare students for the Ohio State Tests and end-ofcourse exams. Math Tutorials offer targeted instruction,
Chapter 12 Transformations: Shapes in Motion
Name Geometry Honors Date Per. Teacher Chapter 12 Transformations: Shapes in Motion 1 Table of Contents Reflections Day 1.... Page 3 Translations Day 2....... Page 10 Rotations/Dilations Day 3.... Page
Congruence of Triangles
Congruence of Triangles You've probably heard about identical twins, but do you know there's such a thing as mirror image twins? One mirror image twin is right-handed while the other is left-handed. And
Chapter 5. Transforming Shapes
Chapter 5 Transforming Shapes It is difficult to walk through daily life without being able to see geometric transformations in your surroundings. Notice how the leaves of plants, for example, are almost
MATHEMATICS CARNIVAL: A VEHICLE FOR ALL TO LEARN CCSSM- GEOMETRIC CONCEPTS!*
MATHEMATICS CARNIVAL: A VEHICLE FOR ALL TO LEARN CCSSM- GEOMETRIC CONCEPTS!* Prof. Vivian La Ferla, ED.D Professor of Mathematics and Computer Science and Educational Studies Rhode Island College Providence,
G-SRT Congruent and Similar
G-SRT Congruent and Similar Triangles Alignments to Content Standards: G-SRT.A.2 Task ABC DEF m( A) = m( D) m( B) = m( E) a. In triangles and below, and. AB = DE Find a sequence of translations, rotations,
UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 1: Investigating Properties of Dilations Instruction
Prerequisite Skills This lesson requires the use of the following skills: operating with fractions, including comple fractions operating with decimals calculating slope determining parallel lines Introduction
Geometry. Instructional Activities:
GEOMETRY Instructional Activities: Geometry Assessment: A. Direct Instruction A. Quizzes B. Cooperative Learning B. Skill Reviews C. Technology Integration C. Test Prep Questions D. Study Guides D. Chapter
PARCC Review. The set of all points in a plane that are equidistant from a given point is called a
Name 1. Select the drop-down menus to correctly complete each sentence. PARCC Review The set of all points in a plane that are equidistant from a given point is called a The given point is called the Radius
YEAR AT A GLANCE Student Learning Outcomes by Marking Period
2014-2015 Term 1 Overarching/general themes: Tools to Build and Analyze Points, Lines and Angles Dates Textual References To Demonstrate Proficiency by the End of the Term Students Will : Marking Period