Lesson 21: Line of Symmetry and Rotational Symmetry

Size: px
Start display at page:

Download "Lesson 21: Line of Symmetry and Rotational Symmetry"

Transcription

1 Lesson 21: Line of Symmetry and Rotational Symmetry Warmup 1. A(1, 6), B(4, 7), C(1, 3) R O,90 r x axis ( ABC) A B C A B C 2. Using the rules, determine the coordinates of the missing point. a) O,90 R ( 6,4) (, ) b) rx 0 ( 3, 5) (, ) c) O,270 R (, ) ( 3, 4) d) r (7, 8) (, ) x axis e) ry axis (, ) (8,4) f) RO, 270 ( 5, 8) (, ) i) T 5,2 (4, 2) = (, ) j) r y=x (1, 5) = (, )

2 Lesson 21: Line of Symmetry and Rotational Symmetry Learning Targets: I can draw the lines of symmetry for a given figure I can identify rotational symmetry within an individual figure. Lesson 21 M1 Definitions 1. occurs when two halves of the figure are mirror images of each other when reflected across a line. 2. The of is the line which divides the figure into two mirror images. Process To determine if a figure has a line of symmetry, fold the figure along the supposed line of symmetry to see if the two halves coincide. A figure has a line of symmetry if the figure can be mapped onto itself by a reflection in the line. Directions: Watch your teacher as s(he) folds each shape to show if the lines that divide the figures in halves are actually the lines of symmetry Square Isosceles Rectangle Example 1) Determine the number of lines of symmetry for each of the following figures and draw them.

3 Not all lines that divide a figure into two congruent halves are lines of symmetry. The diagonal of a rectangle divides the rectangle into two triangles that are congruent (same size and shape). The diagonal of a parallelogram also divides the figure into two triangles that are congruent. Rotational Symmetry of a Figure: Rotational symmetry of a figure is a rotation of the plane that maps the figure back to itself such that the angle of rotation is greater than but less than. **Another word for this rotational symmetry is the symmetry. Which of the polygons above only has identity symmetry?

4 Degree of Rotational Symmetry If a figure can be rotated degrees and map onto itself, it has symmetry. The number of rotated positions in which the object looks exactly the same is the of the rotational symmetry. To calculate the lowest degree of rotational symmetry divide: All other degrees of rotational symmetry are multiples of that value up to and including 360 o. When determining order, the last rotation returns the object to its original position (360). The angles of 0 and 360 are not listed as they are the starting locations. Order 1 implies no true rotational symmetry exists, since a full 360 degree rotation is needed to again display the object with its original appearance. Order 2 implies a duplicate image at a rotation of 180 (divide 360 into 2 equal parts). Order 3 implies a duplicate image at 120 and 240 (divide 360 into 3 equal parts). Order 4 implies a duplicate image at 90, 180, and 270 (divide 360 into 4 equal parts). What is the order of symmetry and the degrees of rotational symmetry for the last 2 figures; flower and the crop circle? Flower: Crop Circle:

5 Example 2) Triangle ABC given below is equilateral. a) What 3 types of symmetry does ABC have? b) What is the order of symmetry? What are the degrees of rotational symmetry of ABC? c) Use your compass to construct two lines of symmetry for ABC. (Connections: A figure has Lines of Symmetry if a perpendicular bisector or angle bisector separates the figure into its own mirror images) d) Label the point of intersection as D, which is the center of rotational symmetry for ABC.

6 Lesson 21: Line of Symmetry and Rotational Symmetry Work Time / Problem Set ABCDE is a regular pentagon. Use the drawing to answer #1-3. A Figure 1 B Problem 1) Draw all lines of symmetry. Locate the center of rotational symmetry. a) What are the degrees of rotational symmetry? E C b) What is the order of the rotational symmetry? D Problem 2) a) Identify the capital letters given that have line(s) of symmetry b) Identify all capital letters that have rotational symmetry. Problem 3) State the lowest degree of rotational symmetry for each figure: Problem 4) Use Figure 3 at right to answer problem 4. a) Draw all lines of symmetry. Locate the center of rotational symmetry. b) What are the degrees of rotational symmetry? c) What is the order of the rotational symmetry? d) What is the total number of symmetries for the figure? e) Shade the figure so that the resulting figure only has 3 possible rotational symmetries (including the identity symmetry). Figure 3

7 Problem 5) Give the order of rotational symmetry and the degrees of rotational symmetry.

8 Pictures to be used to show reflection symmetry and lines of symmetry for smart notebook

39 Symmetry of Plane Figures

39 Symmetry of Plane Figures 39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that

More information

Grade 3 Core Standard III Assessment

Grade 3 Core Standard III Assessment Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in two-dimensional shapes and determine if angles are greater than or less than a right angle (obtuse

More information

11.3 Curves, Polygons and Symmetry

11.3 Curves, Polygons and Symmetry 11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon

More information

Angles that are between parallel lines, but on opposite sides of a transversal.

Angles that are between parallel lines, but on opposite sides of a transversal. GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,

More information

UNIT H1 Angles and Symmetry Activities

UNIT H1 Angles and Symmetry Activities UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)

More information

Estimating Angle Measures

Estimating Angle Measures 1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

More information

Geometry Progress Ladder

Geometry Progress Ladder Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

More information

Target To know the properties of a rectangle

Target To know the properties of a rectangle Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles

More information

Activities Grades K 2 THE FOUR-SQUARE QUILT. Put triangles together to make patterns.

Activities Grades K 2 THE FOUR-SQUARE QUILT. Put triangles together to make patterns. Activities Grades K 2 www.exploratorium.edu/geometryplayground/activities THE FOUR-SQUARE QUILT Put triangles together to make patterns. [45 minutes] Materials: Four-Square Quilt Template (attached) Triangle

More information

Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations

Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Math Buddies -Grade 4 13-1 Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Goal: Identify congruent and noncongruent figures Recognize the congruence of plane

More information

2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?

2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE? MATH 206 - Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of

More information

Selected practice exam solutions (part 5, item 2) (MAT 360)

Selected practice exam solutions (part 5, item 2) (MAT 360) Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On

More information

Which two rectangles fit together, without overlapping, to make a square?

Which two rectangles fit together, without overlapping, to make a square? SHAPE level 4 questions 1. Here are six rectangles on a grid. A B C D E F Which two rectangles fit together, without overlapping, to make a square?... and... International School of Madrid 1 2. Emily has

More information

Lesson 3.1 Duplicating Segments and Angles

Lesson 3.1 Duplicating Segments and Angles Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each

More information

Chapter 18 Symmetry. Symmetry of Shapes in a Plane 18.1. then unfold

Chapter 18 Symmetry. Symmetry of Shapes in a Plane 18.1. then unfold Chapter 18 Symmetry Symmetry is of interest in many areas, for example, art, design in general, and even the study of molecules. This chapter begins with a look at two types of symmetry of two-dimensional

More information

Geometry Module 4 Unit 2 Practice Exam

Geometry Module 4 Unit 2 Practice Exam Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning

More information

Shape Dictionary YR to Y6

Shape Dictionary YR to Y6 Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use

More information

Area. Area Overview. Define: Area:

Area. Area Overview. Define: Area: Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.

More information

1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?

1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above? 1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width

More information

Discovering Math: Exploring Geometry Teacher s Guide

Discovering Math: Exploring Geometry Teacher s Guide Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional

More information

Geometry of 2D Shapes

Geometry of 2D Shapes Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name: GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your

More information

Conjectures. Chapter 2. Chapter 3

Conjectures. Chapter 2. Chapter 3 Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

More information

Quadrilaterals GETTING READY FOR INSTRUCTION

Quadrilaterals GETTING READY FOR INSTRUCTION Quadrilaterals / Mathematics Unit: 11 Lesson: 01 Duration: 7 days Lesson Synopsis: In this lesson students explore properties of quadrilaterals in a variety of ways including concrete modeling, patty paper

More information

New York State Student Learning Objective: Regents Geometry

New York State Student Learning Objective: Regents Geometry New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students

More information

Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?

Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane

More information

Geometry Enduring Understandings Students will understand 1. that all circles are similar.

Geometry Enduring Understandings Students will understand 1. that all circles are similar. High School - Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,

More information

1. Find the length of BC in the following triangles. It will help to first find the length of the segment marked X.

1. Find the length of BC in the following triangles. It will help to first find the length of the segment marked X. 1 Find the length of BC in the following triangles It will help to first find the length of the segment marked X a: b: Given: the diagonals of parallelogram ABCD meet at point O The altitude OE divides

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name: GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

More information

Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids

Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?

More information

GEOMETRY COMMON CORE STANDARDS

GEOMETRY COMMON CORE STANDARDS 1st Nine Weeks Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,

More information

How To Find The Area Of A Shape

How To Find The Area Of A Shape 9 Areas and Perimeters This is is our next key Geometry unit. In it we will recap some of the concepts we have met before. We will also begin to develop a more algebraic approach to finding areas and perimeters.

More information

Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees

Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Angle - a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in

More information

DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.

DEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle. DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent

More information

http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4

http://www.castlelearning.com/review/teacher/assignmentprinting.aspx 5. 2 6. 2 1. 10 3. 70 2. 55 4. 180 7. 2 8. 4 of 9 1/28/2013 8:32 PM Teacher: Mr. Sime Name: 2 What is the slope of the graph of the equation y = 2x? 5. 2 If the ratio of the measures of corresponding sides of two similar triangles is 4:9, then the

More information

Duplicating Segments and Angles

Duplicating Segments and Angles CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty

More information

Geometry: Classifying, Identifying, and Constructing Triangles

Geometry: Classifying, Identifying, and Constructing Triangles Geometry: Classifying, Identifying, and Constructing Triangles Lesson Objectives Teacher's Notes Lesson Notes 1) Identify acute, right, and obtuse triangles. 2) Identify scalene, isosceles, equilateral

More information

Grade 8 Mathematics Geometry: Lesson 2

Grade 8 Mathematics Geometry: Lesson 2 Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

More information

Line Segments, Rays, and Lines

Line Segments, Rays, and Lines HOME LINK Line Segments, Rays, and Lines Family Note Help your child match each name below with the correct drawing of a line, ray, or line segment. Then observe as your child uses a straightedge to draw

More information

Chapter 8 Geometry We will discuss following concepts in this chapter.

Chapter 8 Geometry We will discuss following concepts in this chapter. Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

More information

9 Area, Perimeter and Volume

9 Area, Perimeter and Volume 9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right

More information

SOLIDS, NETS, AND CROSS SECTIONS

SOLIDS, NETS, AND CROSS SECTIONS SOLIDS, NETS, AND CROSS SECTIONS Polyhedra In this section, we will examine various three-dimensional figures, known as solids. We begin with a discussion of polyhedra. Polyhedron A polyhedron is a three-dimensional

More information

Situation: Proving Quadrilaterals in the Coordinate Plane

Situation: Proving Quadrilaterals in the Coordinate Plane Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra

More information

Lesson 2: Circles, Chords, Diameters, and Their Relationships

Lesson 2: Circles, Chords, Diameters, and Their Relationships Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct

More information

Comprehensive Benchmark Assessment Series

Comprehensive Benchmark Assessment Series Test ID #1910631 Comprehensive Benchmark Assessment Series Instructions: It is time to begin. The scores of this test will help teachers plan lessons. Carefully, read each item in the test booklet. Select

More information

Three-Dimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. Two-Dimensional Figures or Plane Figures

Three-Dimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. Two-Dimensional Figures or Plane Figures SHAPE NAMES Three-Dimensional Figures or Space Figures Rectangular Prism Cylinder Cone Sphere Two-Dimensional Figures or Plane Figures Square Rectangle Triangle Circle Name each shape. [triangle] [cone]

More information

/27 Intro to Geometry Review

/27 Intro to Geometry Review /27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the

More information

4. How many integers between 2004 and 4002 are perfect squares?

4. How many integers between 2004 and 4002 are perfect squares? 5 is 0% of what number? What is the value of + 3 4 + 99 00? (alternating signs) 3 A frog is at the bottom of a well 0 feet deep It climbs up 3 feet every day, but slides back feet each night If it started

More information

GEOMETRY. Constructions OBJECTIVE #: G.CO.12

GEOMETRY. Constructions OBJECTIVE #: G.CO.12 GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic

More information

Objectives. Cabri Jr. Tools

Objectives. Cabri Jr. Tools ^Åíáîáíó=NO Objectives To learn how to construct all types of triangles using the Cabri Jr. application To reinforce the difference between a construction and a drawing Cabri Jr. Tools fåíêççìåíáçå `çåëíêìåíáåö

More information

What s Your Angle? (Measurement)

What s Your Angle? (Measurement) The Middle School Math Project What s Your Angle? (Measurement) Objective Using inductive reasoning, students will devise procedures for using a protractor to measure the number of degrees in an angle.

More information

Classifying Lesson 1 Triangles

Classifying Lesson 1 Triangles Classifying Lesson 1 acute angle congruent scalene Classifying VOCABULARY right angle isosceles Venn diagram obtuse angle equilateral You classify many things around you. For example, you might choose

More information

Math 531, Exam 1 Information.

Math 531, Exam 1 Information. Math 531, Exam 1 Information. 9/21/11, LC 310, 9:05-9:55. Exam 1 will be based on: Sections 1A - 1F. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/531fa11/531.html)

More information

Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)

Conjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true) Mathematical Sentence - a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement

More information

Geometry. Higher Mathematics Courses 69. Geometry

Geometry. Higher Mathematics Courses 69. Geometry The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and

More information

The Use of Dynamic Geometry Software in the Teaching and Learning of Geometry through Transformations

The Use of Dynamic Geometry Software in the Teaching and Learning of Geometry through Transformations The Use of Dynamic Geometry Software in the Teaching and Learning of Geometry through Transformations Dynamic geometry technology should be used to maximize student learning in geometry. Such technology

More information

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.

Postulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same. Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

More information

Definitions, Postulates and Theorems

Definitions, Postulates and Theorems Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven

More information

Grade 3 FCAT 2.0 Mathematics Sample Answers

Grade 3 FCAT 2.0 Mathematics Sample Answers Grade FCAT 2.0 Mathematics Sample Answers This booklet contains the answers to the FCAT 2.0 Mathematics sample questions, as well as explanations for the answers. It also gives the Next Generation Sunshine

More information

Most popular response to

Most popular response to Class #33 Most popular response to What did the students want to prove? The angle bisectors of a square meet at a point. A square is a convex quadrilateral in which all sides are congruent and all angles

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A. Tuesday, August 13, 2002 8:30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A. Tuesday, August 13, 2002 8:30 to 11:30 a.m. The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A Tuesday, August 13, 2002 8:30 to 11:30 a.m., only Print Your Name: Print Your School s Name: Print your name and the

More information

Intermediate Math Circles October 10, 2012 Geometry I: Angles

Intermediate Math Circles October 10, 2012 Geometry I: Angles Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,

More information

Geometry Course Summary Department: Math. Semester 1

Geometry Course Summary Department: Math. Semester 1 Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give

More information

Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons

Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons I. ABSTRACT This unit contains lessons that focus on geometric

More information

Objective To guide exploration of the connection between reflections and line symmetry. Assessment Management

Objective To guide exploration of the connection between reflections and line symmetry. Assessment Management Line Symmetry Objective To guide exploration of the connection between reflections and line symmetry. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

More information

CSU Fresno Problem Solving Session. Geometry, 17 March 2012

CSU Fresno Problem Solving Session. Geometry, 17 March 2012 CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfd-prep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news

More information

Week 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test

Week 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan

More information

The Area of a Triangle Using Its Semi-perimeter and the Radius of the In-circle: An Algebraic and Geometric Approach

The Area of a Triangle Using Its Semi-perimeter and the Radius of the In-circle: An Algebraic and Geometric Approach The Area of a Triangle Using Its Semi-perimeter and the Radius of the In-circle: An Algebraic and Geometric Approach Lesson Summary: This lesson is for more advanced geometry students. In this lesson,

More information

Geometry Regents Review

Geometry Regents Review Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest

More information

How to fold simple shapes from A4 paper

How to fold simple shapes from A4 paper How to fold simple shapes from 4 paper ndrew Jobbings www.arbelos.co.uk 18 February 2012 ontents Introduction 1 Square 2 Equilateral triangle 3 Rhombus 5 Regular hexagon 6 Kite 7 Why do the methods work?

More information

PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

More information

SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4

SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4 SGS4.3 Stage 4 Space & Geometry Part A Activity 2-4 Exploring triangles Resources required: Each pair students will need: 1 container (eg. a rectangular plastic takeaway container) 5 long pipe cleaners

More information

Vector Notation: AB represents the vector from point A to point B on a graph. The vector can be computed by B A.

Vector Notation: AB represents the vector from point A to point B on a graph. The vector can be computed by B A. 1 Linear Transformations Prepared by: Robin Michelle King A transformation of an object is a change in position or dimension (or both) of the object. The resulting object after the transformation is called

More information

Drawing Lines of Symmetry Grade Three

Drawing Lines of Symmetry Grade Three Ohio Standards Connection Geometry and Spatial Sense Benchmark H Identify and describe line and rotational symmetry in two-dimensional shapes and designs. Indicator 4 Draw lines of symmetry to verify symmetrical

More information

Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

More information

Geometry - Semester 2. Mrs. Day-Blattner 1/20/2016

Geometry - Semester 2. Mrs. Day-Blattner 1/20/2016 Geometry - Semester 2 Mrs. Day-Blattner 1/20/2016 Agenda 1/20/2016 1) 20 Question Quiz - 20 minutes 2) Jan 15 homework - self-corrections 3) Spot check sheet Thales Theorem - add to your response 4) Finding

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 24, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

More information

GEOMETRY CONCEPT MAP. Suggested Sequence:

GEOMETRY CONCEPT MAP. Suggested Sequence: CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons

More information

Classifying Quadrilaterals

Classifying Quadrilaterals 1 lassifying Quadrilaterals Identify and sort quadrilaterals. 1. Which of these are parallelograms?,, quadrilateral is a closed shape with 4 straight sides. trapezoid has exactly 1 pair of parallel sides.

More information

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points. 6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which

More information

Teaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons

Teaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons CIRCLE FOLDING Teaching Guidelines Subject: Mathematics Topics: Geometry (Circles, Polygons) Grades: 4-6 Concepts: Property Diameter Radius Chord Perimeter Area Knowledge and Skills: Can specify defining

More information

Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.

Circumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice. Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

TImath.com. Geometry. Points on a Perpendicular Bisector

TImath.com. Geometry. Points on a Perpendicular Bisector Points on a Perpendicular Bisector ID: 8868 Time required 40 minutes Activity Overview In this activity, students will explore the relationship between a line segment and its perpendicular bisector. Once

More information

Transformations Worksheet. How many units and in which direction were the x-coordinates of parallelogram ABCD moved? C. D.

Transformations Worksheet. How many units and in which direction were the x-coordinates of parallelogram ABCD moved? C. D. Name: ate: 1. Parallelogram ABC was translated to parallelogram A B C. 2. A shape is shown below. Which shows this shape transformed by a flip? A. B. How many units and in which direction were the x-coordinates

More information

1 Solution of Homework

1 Solution of Homework Math 3181 Dr. Franz Rothe February 4, 2011 Name: 1 Solution of Homework 10 Problem 1.1 (Common tangents of two circles). How many common tangents do two circles have. Informally draw all different cases,

More information

Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain

Georgia Online Formative Assessment Resource (GOFAR) AG geometry domain AG geometry domain Name: Date: Copyright 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 36 ) 1. Amy drew a circle graph to represent

More information

GeoGebra. 10 lessons. Gerrit Stols

GeoGebra. 10 lessons. Gerrit Stols GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any

More information

Lesson 1.1 Building Blocks of Geometry

Lesson 1.1 Building Blocks of Geometry Lesson 1.1 Building Blocks of Geometry For Exercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q 2. NQ. 3. nother name for NS is. 4. S is the of SQ. 5. is the midpoint of. 6. NS.

More information

Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures.

Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures. Geometry: Unit 1 Vocabulary 1.1 Undefined terms Cannot be defined by using other figures. Point A specific location. It has no dimension and is represented by a dot. Line Plane A connected straight path.

More information

Unit 2 - Triangles. Equilateral Triangles

Unit 2 - Triangles. Equilateral Triangles Equilateral Triangles Unit 2 - Triangles Equilateral Triangles Overview: Objective: In this activity participants discover properties of equilateral triangles using properties of symmetry. TExES Mathematics

More information

Chapter 6 Notes: Circles

Chapter 6 Notes: Circles Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment

More information

37 Basic Geometric Shapes and Figures

37 Basic Geometric Shapes and Figures 37 Basic Geometric Shapes and Figures In this section we discuss basic geometric shapes and figures such as points, lines, line segments, planes, angles, triangles, and quadrilaterals. The three pillars

More information

Algebra Geometry Glossary. 90 angle

Algebra Geometry Glossary. 90 angle lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:

More information

Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

More information

Star and convex regular polyhedra by Origami.

Star and convex regular polyhedra by Origami. Star and convex regular polyhedra by Origami. Build polyhedra by Origami.] Marcel Morales Alice Morales 2009 E D I T I O N M O R A L E S Polyhedron by Origami I) Table of convex regular Polyhedra... 4

More information