Coordinate Coplanar Distance Formula Midpoint Formula


 Stephen Taylor
 2 years ago
 Views:
Transcription
1 G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the oneand twodimensional coordinate systems to verify geometric conjectures. G.2(A) determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one and twodimensional coordinate systems, including finding the midpoint. Determine the coordinates of a point that is given fractional distance from either endpoint of a line segment. Find the coordinates of point P along the directed line segment AB so that AP to PB is the ratio 2 to 6 when A(3,2), B(5,4). Correct answer: P(1,0.5) Coordinate Coplanar Distance Formula Midpoint Formula Compare the methods of counting lines on the number line or coordinate plane and using the midpoint or distance formula to calculate the distances. Big Ideas 3.5, Example 2 Connects to G.2B Page 1
2 G.2(B) derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines. Readiness Standard Use slopes to determine whether the lines are parallel, perpendicular or neither. Comparing equations of lines, determine whether lines are parallel, intersect or coincide. Prove lines are parallel given angle information. Prove and apply theorems about perpendicular lines State whether the graphs of the following equations are parallel, perpendicular, intersecting or coincide Ex. 5x3y = 7 y= 3/5x + 8 Correct answer: Perpendicular Midpoint Slope Parallel Perpendicular Interesting lines Coincide Slope intercept form y intercept Use distance formula to find the distance between 2 points. Find coordinates of the midpoint of a segment on a coordinate plane. Find endpoint given an endpoint and a midpoint. Demonstrate through use and problem solving. 3.4, 3.5, 3.6, 5.1 Misconceptions: The student may substitute the x and yvalues incorrectly when using the formulas. The student may divide a value by 2 instead of taking the square root when using the distance formula. The student may add the xvalue to the yvalue, instead of computing the sum of the xvalues and computing the sum of the yvalues before dividing by 2 in the midpoint formula. The student may incorrectly write the ratio of the slope of a line as the ratio of horizontal change divided by vertical change Page 2
3 G.2(C) determine an equation of a line parallel or perpendicular to a given line that passes through a given point. Readiness Standard Write and compare equations of lines. Write the equation of a line parallel and perpendicular to a given line through the given point. The graph of line g is shown below. What equation describes a line parallel to g that has a yintercept at (0,1)? Correct answer: 1 y x 1 Released EOC 2013 Q#25 2 Slope intercept form y intercept perpendicular bisector coordinate Review the relationships between slopes of parallel and perpendicular lines. Provide students with graphic organizers to help sort parallel and perpendicular lines. 3.5, 3.6 Google Drive: G.2C Task Activity Use Guided Practice G.2C Task Activity in the Google drive for class practice. Misconceptions: The student may use the slope formula incorrectly horizontalchange (ie: instead of vertical change ). verticalchange horizontal change The student may think the slopes of perpendicular line are only opposite values instead of opposite reciprocals Page 3
4 G.(3) Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and nonrigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity). G.3(A) describe and perform transformations of figures in a plane using coordinate notation. Describe transformations of figures in a plane using coordinate notation. Parallelogram ABCD was transformed to form parallelogram A B C D. Transformation Translation Reflection Rotation Big Ideas 4.1 Dilation Connects to G.3B Perform transformations of figures in a plane using coordinate notation. Which rule describes the transformation that was used to form parallelogram A B C D? F. ( x, y) ( x, y) G. ( x, y) ( x, y) H. ( x, y) ( x 6, y) J. ( x, y) ( x, y 3) (x, y3) Correct answer: J Adapted from Released EOC 2013 Q#40 Use three column notes to provide transformation in a plane in one column, verbal description in another, coordinate notation in third. Google Drive: Graphic Organizer Card Sort Activity Engaging p. 45 (18.pdf) Page 4
5 G.3(B) determine the image or preimage of a given twodimensional figure under a composition of rigid transformations, a composition of nonrigid transformations, and a composition of both, including dilations where the center can be any point in the plane. Readiness Standard Determine the image preimage of a given twodimensional figure under a composition of rigid nonrigid both transformations. Determine the image preimage of a given twodimensional figure that includes dilations where the center can be any point in the plane. ΔABC has vertices A(3, 1), B (2,  1), and C (0, 2). Reflect the figure across the yaxis and then translate it 3 units down and 4 units to the right. What are the coordinates of the image? Correct Answer: A (7, 2), B (2, 4), C (4, 1) Image Preimage Transformation Translation Reflection Rotation Dilation Composition Center of Dilation Rigid transformation Non/Congruent figures Center of dilation at origin: Multiply coordinates of preimage by scale factor Center of dilation not at origin: use slope to find image points Stress use of prime notation for image points Big Ideas 4.1, 4.2, 4.6 Engaging p. 57 (23.pdf) & p. 59 (24.pdf) Misconceptions: The student may not be able to distinguish the difference between image and preimage The student may think the origin is the only point that can be the center for dilations Page 5
6 G.3(C) identify the sequence of transformations that will carry a given preimage onto an image on and off the coordinate plane. Connects to G.3B Identify the sequence of transformations that will carry a given preimage onto an image on the coordinate plane. Identify the sequence of transformations that will carry a given preimage onto an image off the coordinate plane. Jake took pictures of Ana s flag while she was practicing her routine for the football game, as shown below. Which of the following best describes the movement of the flag from picture to picture? A. Reflection, rotation, translation B. Rotation, translation, translation C. Rotation, translation, dilation D. Reflection, translation, translation Image Preimage Transformation Translation Reflection Rotation Dilation Composition Center of Dilation Point of rotation Scale factor Similarity Demonstrate that the order of the transformations matters. Include a variety of examples where students identify the sequence of transformations. There may be several different methods for transforming the same preimage into an image. Big Ideas 4.4, 4.6 G.3(D) identify and distinguish between reflectional and rotational symmetry in a plane figure. Connect to G.3B Identify reflectional symmetry in a plane figure. Identify rotational symmetry in a plane figure. Distinguish between reflectional and rotational symmetry in a plane figure. Answer: A Tell whether the figure has rotational and/or reflectional symmetry. Rotational yes Reflectional no Symmetry Rotational symmetry Reflectional symmetry Line of reflection Line of symmetry Center of rotation Angle of rotation Center of symmetry Reflectional: over a line Rotational: about a point Make sure students label the vertices Big Ideas 4.2, Page 6
7 G.(5) Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures. The student is expected to: G.5(A) investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools. Readiness Standard Use the exterior angle theorem to find angle measures Find the measure of F Exterior angles theorem Exterior angle Interior angle Remote interior angles Triangle sum theorem Use both numeric and algebraic expressions to find missing angles measures 5.2 Misconceptions: The student may make a conjecture based on limited investigation of patterns. The student may randomly state a conjecture without investigating and recognizing patterns. The student may not know how to use a construction to make a conjecture. The student may not be able to perform constructions correctly. The student may not state a conjecture using precise geometric vocabulary. Engaging p. 79 (32.pdf) Page 7
8 G.5(B) construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge. Connects to G.5A, G.6A G.5(C) use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships. Connects: G.5A, G.6A Use a compass and a straight edge to construct: Perpendicular lines The perpendicular bisector of a line segment using a compass and a straightedge. A line parallel to a given line through a point not on a line Use constructions, Congruent segments Congruent angles Angle bisectors Perpendicular bisectors To make conjectures about geometric relationships. What construction is shown in the accompanying diagram? A. The bisector of angle PJR. B. The midpoint of line PQ C. The Perpendicular bisector of line segment PQ. D. A perpendicular line to PQ through point J. Answer: C Compass Construction Drawing Sketch Straight Edge Angle bisector Bisect Congruent Congruent angles Congruent segments Constructions Perpendicular Perpendicular bisector Focus on constructing geometric figures with only a straight edge and a compass. Ensure students can construct congruent segments. Use two column notes that have students write the steps needed to construct on one side while performing the task of construction in the other. As students construct figures, they should also describe what they see and explain why the construction works. Big Ideas 3.3, com/tocs/constructionsto c.html 3.3, 3.4, Page 8
9 G.(6) Proof and congruence. The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as twocolumn, paragraph, and flow chart. The student is expected to: G.6(A) verify theorems about angles formed by the intersection of lines Find the value of x and solve problems involving parallel lines and vertical Find the value of x to verify that the lines are parallel Alternate Exterior Angles Alternate Interior Substitute different values to verify angle measures. Big Ideas 3.3, 3.4 and line segments, angles Angles Use manipulatives and including vertical Coplanar technology to draw angles, and angles Corresponding Angles conclusions and formed by parallel lines Diagonal discover relationships cut by a transversal and Graph segments and find the Parallel Lines about parallel lines and prove equidistance perpendicular bisector using PQ is shown on the coordinate Perpendicular Lines their properties between the endpoints the slope and midpoint SameSide Interior of a segment and points formulas grid below. The coordinates of P Angles Stress the importance of on its perpendicular and Q are integers. Segment slopes perpendicular to bisector and apply these Skew Lines a line (opposite relationships to solve Transversal reciprocal) problems. Readiness Standard Point (x, y) lies on the perpendicular bisector of PQ. What is the value of x? Correct answer: 2.5 Released EOC 2013 Q#10 bisector Slope Midpoint Coordinates Use distance formula to find the distance between 2 points and the midpoint Find coordinates of the midpoint of a segment on a coordinate plane. Misconceptions: The student may not use logical reasoning correctly to work through proofs. The student may not apply justification to support statements in a twocolumn proof Page 9
10 G.6(C) apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles. Connects to G.6B, G.3B G.6(D) verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems. Connects to G.5A Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures corresponding sides (of congruent figures) corresponding angles (of congruent figures) Verify theorems about the relationships in triangles: Including the sum of interior angles. (The rest of this SE is addressed in the 3 rd and 4 th grading periods.) Find the missing angle measure in triangles Determine relationships of angles and sides when bisectors, medians and altitudes are drawn in triangles. Use AAS to explain why the triangles are congruent. Answer: A D, BEA CED, BE CE B is the midpoint of A B D D is the midpoint of and AE = 21. Find BD. The diagram is not to scale. C E Corollary Corresponding Angles Corresponding Polygons Corresponding Sides Included Angle Included Side Interior Triangle Rigidity SAS SSS ASA AAS AL Midsegment Midpoint Congruent Parallel Isosceles triangle equilateral triangle Equidistant Base angles Medians, bisectors Hinge theorem Inequality Perpendicular bisector Altitude Students should mark pictures with congruence to be able to easily determine how the triangles are congruent i.e. AAS, SAS, ASA Verify relationships in triangles including triangle sum theorem, base angles of isosceles triangles and angles in equilateral triangles. In an Isosceles triangle, have students discover Median, angle bisector, perpendicular bisector are all the same line. Find the value of the midsegment given the parallel side of the triangle. Use both algebraic expressions and numeric values when solving 4.4, , 5.4 Engaging p (39.pdf) Page 10
11 G.7 Proof and Congruence: The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as twocolumn, paragraph, and flow chart. The student is expected to: G.7(A) apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides. Apply the definition of similarity in terms of a dilation to identify similar figures. Isosceles trapezoid JKLM is shown below. Congruent corresponding angles Dilation Proportional Similar figures Similarity Utilize a graphic organizer to compare the properties of congruence transformation and similarity 4.6 transformations. Connects to G.3B, G.7B (The rest of this SE is addressed in the 4 th grading period.) If the dimensions of the trapezoid JKLM are multiplied by a scale factor of f to create trapezoid J K L M, which statement is true? F. Trapezoid J K L M contains two base angles measuring 30 each. G. The longer base of trapezoid J K L M is 56f units. H. The bases of trapezoid J K L M have lengths of 22 units and 39 units. J. Trapezoid J K L M contains two base angles measuring (120 f ) each. Correct answer: G Released EOC 2013 Q# Page 11
Chapter 1: Essentials of Geometry
Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,
More informationGeometry Course Summary Department: Math. Semester 1
Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give
More informationGeometry Enduring Understandings Students will understand 1. that all circles are similar.
High School  Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,
More informationGEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
More informationGeometry Chapter 1 Vocabulary. coordinate  The real number that corresponds to a point on a line.
Chapter 1 Vocabulary coordinate  The real number that corresponds to a point on a line. point  Has no dimension. It is usually represented by a small dot. bisect  To divide into two congruent parts.
More informationGEOMETRY COMMON CORE STANDARDS
1st Nine Weeks Experiment with transformations in the plane GCO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point,
More informationA Correlation of Pearson Texas Geometry Digital, 2015
A Correlation of Pearson Texas Geometry Digital, 2015 To the Texas Essential Knowledge and Skills (TEKS) for Geometry, High School, and the Texas English Language Proficiency Standards (ELPS) Correlations
More informationGeometry. Higher Mathematics Courses 69. Geometry
The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and
More informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationNew York State Student Learning Objective: Regents Geometry
New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students
More informationWeek 1 Chapter 1: Fundamentals of Geometry. Week 2 Chapter 1: Fundamentals of Geometry. Week 3 Chapter 1: Fundamentals of Geometry Chapter 1 Test
Thinkwell s Homeschool Geometry Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Geometry! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan
More informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More information0810ge. Geometry Regents Exam 0810
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 identify
More informationCentroid: The point of intersection of the three medians of a triangle. Centroid
Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:
More information1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
More informationCurriculum Map by Block Geometry Mapping for Math Block Testing 20072008. August 20 to August 24 Review concepts from previous grades.
Curriculum Map by Geometry Mapping for Math Testing 20072008 Pre s 1 August 20 to August 24 Review concepts from previous grades. August 27 to September 28 (Assessment to be completed by September 28)
More informationDefinitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
More information2, 3 1, 3 3, 2 3, 2. 3 Exploring Geometry Construction: Copy &: Bisect Segments & Angles Measure & Classify Angles, Describe Angle Pair Relationship
Geometry Honors Semester McDougal 014015 Day Concepts Lesson Benchmark(s) Complexity Level 1 Identify Points, Lines, & Planes 11 MAFS.91.GCO.1.1 1 Use Segments & Congruence, Use Midpoint & 1/1 MAFS.91.GCO.1.1,
More informationNorth Carolina Math 2
Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4.
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 16, 2012 8:30 to 11:30 a.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS Curriculum TERM 1 CONTENT Properties of numbers Describe the real number system by recognizing, defining and distinguishing properties of: Natural numbers Whole numbers
More informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
More informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationMathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
More informationUnit 3: Triangle Bisectors and Quadrilaterals
Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties
More information55 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 220 points.
Geometry Core Semester 1 Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which topics you need to review most carefully. The unit
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationSOLVED PROBLEMS REVIEW COORDINATE GEOMETRY. 2.1 Use the slopes, distances, line equations to verify your guesses
CHAPTER SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY For the review sessions, I will try to post some of the solved homework since I find that at this age both taking notes and proofs are still a burgeoning
More information65 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.
ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. A rhombus is a parallelogram with all four sides congruent. So, Then, is an isosceles triangle. Therefore, If a parallelogram
More informationStudent Name: Teacher: Date: District: MiamiDade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1
Student Name: Teacher: Date: District: MiamiDade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the
More informationPOTENTIAL REASONS: Definition of Congruence:
Sec 6 CC Geometry Triangle Pros Name: POTENTIAL REASONS: Definition Congruence: Having the exact same size and shape and there by having the exact same measures. Definition Midpoint: The point that divides
More informationThe 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 informationConjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence  a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
More informationGeometry 1. Unit 3: Perpendicular and Parallel Lines
Geometry 1 Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3 3.1 Lines and Angles Lines and Angles Parallel Lines Parallel lines are lines that are coplanar and do not intersect. Some examples
More informationMathematics Task Arcs
Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number
More informationGEOMETRY. Constructions OBJECTIVE #: G.CO.12
GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More informationFinal Review Geometry A Fall Semester
Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over
More informationThe 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 information7. 6 Justifying Constructions
31 7. 6 Justifying Constructions A Solidify Understanding Task CC BY THOR https://flic.kr/p/9qkxv Compass and straightedge constructions can be justified using such tools as: the definitions and properties
More informationMathematics Geometry Unit 1 (SAMPLE)
Review the Geometry sample yearlong scope and sequence associated with this unit plan. Mathematics Possible time frame: Unit 1: Introduction to Geometric Concepts, Construction, and Proof 14 days This
More informationQuadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid
Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,
More informationABC is the triangle with vertices at points A, B and C
Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry  symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the
More informationQuadrilaterals 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 information116 Chapter 6 Transformations and the Coordinate Plane
116 Chapter 6 Transformations and the Coordinate Plane Chapter 61 The Coordinates of a Point in a Plane Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive
More informationUnit 6 Grade 7 Geometry
Unit 6 Grade 7 Geometry Lesson Outline BIG PICTURE Students will: investigate geometric properties of triangles, quadrilaterals, and prisms; develop an understanding of similarity and congruence. Day Lesson
More informationGeorgia Standards of Excellence Curriculum Frameworks. Mathematics. GSE Geometry Unit 2: Similarity, Congruence, and Proofs
Georgia Standards of Excellence Curriculum Frameworks Mathematics GSE Geometry Unit 2: Similarity, Congruence, and Proofs Unit 2 Similarity, Congruence, and Proofs Table of Contents OVERVIEW... 3 STANDARDS
More informationCAMI Education linked to CAPS: Mathematics
 1  TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to
More informationThe 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 informationStudents will understand 1. use numerical bases and the laws of exponents
Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?
More informationLesson 2: Circles, Chords, Diameters, and Their Relationships
Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More informationNumber Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
More informationThe 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 informationA. 3y = 2x + 1. y = x + 3. y = x  3. D. 2y = 3x + 3
Name: Geometry Regents Prep Spring 2010 Assignment 1. Which is an equation of the line that passes through the point (1, 4) and has a slope of 3? A. y = 3x + 4 B. y = x + 4 C. y = 3x  1 D. y = 3x + 1
More informationwith functions, expressions and equations which follow in units 3 and 4.
Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model
More informationCircle Name: Radius: Diameter: Chord: Secant:
12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane
More informationFlorida Geometry EOC Assessment Study Guide
Florida Geometry EOC Assessment Study Guide The Florida Geometry End of Course Assessment is computerbased. During testing students will have access to the Algebra I/Geometry EOC Assessments Reference
More informationGeorgia Standards of Excellence Mathematics
Georgia Standards of Excellence Mathematics Standards GSE Geometry K12 Mathematics Introduction Georgia Mathematics focuses on actively engaging the student in the development of mathematical understanding
More information/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
More informationMcDougal Littell California:
McDougal Littell California: PreAlgebra Algebra 1 correlated to the California Math Content s Grades 7 8 McDougal Littell California PreAlgebra Components: Pupil Edition (PE), Teacher s Edition (TE),
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationPerformance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will
Performance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will discover and prove the relationship between the triangles
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, June 19, :15 a.m. to 12:15 p.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 19, 2013 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
More informationDate: Period: Symmetry
Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, January 26, 2016 1:15 to 4:15 p.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, January 26, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The possession or use of any communications
More information1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.
Quadrilaterals  Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals  Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,
More informationSupport Materials for Core Content for Assessment. Mathematics
Support Materials for Core Content for Assessment Version 4.1 Mathematics August 2007 Kentucky Department of Education Introduction to Depth of Knowledge (DOK)  Based on Norman Webb s Model (Karin Hess,
More informationGeometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: Activity 24
Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: ctivity 24 esources: Springoard Geometry Unit Overview In this unit, students will study formal definitions of basic figures,
More information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More informationCongruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key
Instruction Goal: To provide opportunities for students to develop concepts and skills related to identifying and constructing angle bisectors, perpendicular bisectors, medians, altitudes, incenters, circumcenters,
More informationChapter 5: Relationships within Triangles
Name: Chapter 5: Relationships within Triangles Guided Notes Geometry Fall Semester CH. 5 Guided Notes, page 2 5.1 Midsegment Theorem and Coordinate Proof Term Definition Example midsegment of a triangle
More informationSelected 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 informationSemester Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Are O, N, and P collinear? If so, name the line on which they lie. O N M P a. No,
More informationGeometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
More informationGeometry, Final Review Packet
Name: Geometry, Final Review Packet I. Vocabulary match each word on the left to its definition on the right. Word Letter Definition Acute angle A. Meeting at a point Angle bisector B. An angle with a
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationGeometry: 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 informationSum of the interior angles of a nsided Polygon = (n2) 180
5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a nsided Polygon = (n2) 180 What you need to know: How to use the formula
More informationUnit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period
Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,
More informationAlgebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms  Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
More informationPolygons are figures created from segments that do not intersect at any points other than their endpoints.
Unit #5 Lesson #1: Polygons and Their Angles. Polygons are figures created from segments that do not intersect at any points other than their endpoints. A polygon is convex if all of the interior angles
More informationThe 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 information5.1 Midsegment Theorem and Coordinate Proof
5.1 Midsegment Theorem and Coordinate Proof Obj.: Use properties of midsegments and write coordinate proofs. Key Vocabulary Midsegment of a triangle  A midsegment of a triangle is a segment that connects
More informationGlencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 33, 58 84, 87 16, 49
Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 68 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,
More informationDuplicating 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 informationUtah Core Curriculum for Mathematics
Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions
More informationPUBLIC SCHOOLS OF EDISON TOWNSHIP OFFICE OF CURRICULUM AND INSTRUCTION GEOMETRY HONORS. Middle School and High School
PUBLIC SCHOOLS OF EDISON TOWNSHIP OFFICE OF CURRICULUM AND INSTRUCTION GEOMETRY HONORS Length of Course: Elective/Required: Schools: Term Required Middle School and High School Eligibility: Grades 812
More informationTriangle Congruence and Similarity A CommonCoreCompatible Approach
Triangle Congruence and Similarity A CommonCoreCompatible Approach The Common Core State Standards for Mathematics (CCSSM) include a fundamental change in the geometry program in grades 8 to 10: geometric
More informationMathematics programmes of study: key stage 3. National curriculum in England
Mathematics programmes of study: key stage 3 National curriculum in England September 2013 Purpose of study Mathematics is a creative and highly interconnected discipline that has been developed over
More informationPrentice Hall Algebra 2 2011 Correlated to: Colorado P12 Academic Standards for High School Mathematics, Adopted 12/2009
Content Area: Mathematics Grade Level Expectations: High School Standard: Number Sense, Properties, and Operations Understand the structure and properties of our number system. At their most basic level
More informationGeometry Chapter 5 Relationships Within Triangles
Objectives: Section 5.1 Section 5.2 Section 5.3 Section 5.4 Section 5.5 To use properties of midsegments to solve problems. To use properties of perpendicular bisectors and angle bisectors. To identify
More informationUnit 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 informationNEW MEXICO Grade 6 MATHEMATICS STANDARDS
PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical
More informationSituation: Proving Quadrilaterals in the Coordinate Plane
Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More information