A Different Look at Trapezoid Area Prerequisite Knowledge


 August Walton
 1 years ago
 Views:
Transcription
1 Prerequisite Knowledge Conditional statement an ifthen statement (If A, then B) Converse the two parts of the conditional statement are reversed (If B, then A) Parallel lines are lines in the same plane that do not intersect. Skew lines are lines not in the same plane that do not intersect. A transversal is a line (or line segment) that cuts across or intersects two or more lines in the same plane (usually parallel but not necessarily). t c d ABOVE: c and d are parallel; t is the transversal Two parallel lines cut by a transversal form several types of angles (defined in pairs) that are congruent. Corresponding angles are pairs of angles that are on the same side of the transversal and occupy the same location at each intersection (ex: angles 3 and 7; angles 6 and 2). If the transversal intersects parallel lines, then the corresponding angles are congruent. Alternate interior angles lie inside the parallel lines and are on opposite sides of the transversal (ex: angles 3 and 6; angles 5 and 4). If the transversal intersects parallel lines, then the alternate interior angles are congruent. Alternate exterior angles lie outside the parallel lines and are on opposite sides of the transversal (ex: angles 1 and 8; angles 2 and 7). If the transversal intersects parallel lines, then the alternate exterior angles are congruent. The converses for the above are true. Ex: If two lines in the same plane are intersected so that the corresponding angles are equal, then the lines are parallel.
2 Prerequisite Knowledge (page 2) a b c d ABOVE: a and b are parallel; c and d are parallel; any of the 4 can be a transversal Two parallel lines cut by a transversal form several types of angles (defined in pairs) that are congruent. Corresponding angles are pairs of angles that are on the same side of the transversal and occupy the same location at each intersection (ex: angles 3 and 7; angles 9 and 13). If the transversal intersects parallel lines, then the corresponding angles are congruent. Alternate interior angles lie inside the parallel lines and are on opposite sides of the transversal (ex: angles 3 and 6; angles 12 and 13). If the transversal intersects parallel lines, then the alternate interior angles are congruent. Alternate exterior angles lie outside the parallel lines and are on opposite sides of the transversal (ex: angles 1 and 8; angles 2 and 7). If the transversal intersects parallel lines, then the alternate exterior angles are congruent. Note: There are other possibilities in the diagram. Ex: If lines a and b are the parallel lines and d is the transversal, then angles 5 and 13 are corresponding angles. Note: The names of angles (as a single angle or as a pair) are dependent on the context. For example, angle 12 is an interior angle if b is a transversal with c and d as the parallel lines, but angle 12 is an exterior angle if c is the transversal with a and b as the parallel lines. TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 2
3 Prerequisite Knowledge (page 3) A midpoint lies exactly halfway between the two endpoints of a line segment. A polygon is a set of line segments in the same plane, each connected endtoend to form a closed shape. The polygon is made up of the segments themselves. The inside of the polygon is the interior and the outside is the exterior. A quadrilateral is a 4sided polygon four line segments in the same plane linked endtoend to create a closed figure. A trapezoid is a special type of quadrilateral that has exactly one pair of parallel sides. **** (However, another definition states that a trapezoid is a quadrilateral that has at least one pair of parallel sides by this definition, a parallelogram may also be considered a trapezoid.) In a trapezoid, the median is the segment that connects the midpoints of the two nonparallel sides. The median also bisects the height. A parallelogram is a special type of quadrilateral that has exactly two pair of parallel sides. Parallelograms have several special properties: Both pairs of opposite sides of a parallelogram are congruent. The opposite angles of a parallelogram are congruent. Each pair of the opposite sides of a parallelogram is both congruent and parallel. Given a quadrilateral, if you can establish that any of the above are true, then the quadrilateral is a parallelogram. Any side of a parallelogram can be considered a base. The altitude (or height) of a parallelogram is the perpendicular distance from the base to the opposite side (which may have to be extended). Symbols used to show equal measures TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 3
4 Developing the Parallelogram Formula Work in groups at your respective tables. In the group resource packet, you will find parallelogram figures on vanillacolored stock. Each student is to take one of these and follow the instructions. TASK: a) Mark all the pairs of angles and/or sides that have equal measures. Discuss with your group why you know they are equal measures. b) Using the scissors provided, cut along each edge so that the figure is a parallelogram. c) Cut the parallelogram along the segment labeled as h (height) so that there are two new figures. d) Join the two figures so that they form a special type of quadrilateral (A trapezoid is possible, but that is not the solution here). What is the name of this quadrilateral? How do you know that it is this special quadrilateral? e) How do the area of the original parallelogram and that of the new quadrilateral compare? Why is that? f) What is the formula for the area of the special new quadrilateral? (This was something learned in previous math classes.) g) Use the area formula for the new quadrilateral to find the formula for the area of the original parallelogram. TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 4
5 Making Connections Work in groups at your respective tables. In the group resource packet, you will find trapezoid figures on lavender stock. The segments b 1 and b 2 are parallel. Each student is to take one of these and follow the instructions. TASK: 1) Observe the trapezoid. a) Notice (and remember) that there are transversals intersecting parallel lines. Also notice that although the lines are extended past the points of intersection that a trapezoid is formed. b) Find the midpoint of each of the two nonparallel sides. (Use the rulers found in the group resource packet.) Measure from the vertices, not from the end of the segments. c) Connect those two points with a line segment. This horizontal segment is a median, and it connects the midpoints of the two nonparallel sides and also bisects the height. d) Label all the matching pairs of segments and angles that you know are equal measures. (This is a very important step!!!) e) Using the scissors in the group resource packet, cut along each edge so that the extra lengths are removed and the remaining figure is a trapezoid. Next, use the scissors to cut the trapezoid into two pieces by cutting along the median. 2) Take the two pieces and join the nonparallel sides in such a way as to form a new 4 sided figure. 3) What type of figure is this new quadrilateral? How could you prove your assertion? TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 5
6 4) How does the area of the new figure compare to the original trapezoid? Why is that? 5) Remember that the original figure was a trapezoid. How does the height of the new figure compare to the original trapezoid? 6) Using this information and the labeling of the bases of the new figure, use the parallelogram area formula to determine a formula for the area of a trapezoid. Justify/prove your answer. TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 6
7 New Perspective The area of a trapezoid is given by the formula below: A = 1 2 h ( b 1 + b 2 ) 1) Review your previous work and perspective in deriving the trapezoid area formula, especially the transformation of the parallelogram formula to the trapezoid formula. 2) Edit/Reorganize the formula below to match the interpretation and write down an explanation or justification. A = 1 2 h ( b 1 + b 2 ) TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 7
8 Perspective Summary The activity began with a trapezoid. The height was cut into two pieces and the two resulting parts were joined to make a new figure that can be proven to be a parallelogram. Since there was nothing added or destroyed on the figures, the area is still the same. This perspective can then be expressed to show that we take the new height (which is one half the original trapezoid height) times the base of the new parallelogram which is represented by ( b 1 + b 2 ). A = b h A = h b Original transformed to A = [ 1 2 h ] ( b 1 + b 2 ) new A = 1 2 h ( b 1 + b 2 ) TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 8
9 b 1 b 2 b 1 b 2 TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 9
10 b 1 b 2 b 1 b 2 TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 10
11 b 1 b 2 b 1 b 2 TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 11
12 h b h b h b TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 12
13 Addressed TEKS TEKS Objective for the lesson: Geometry G.2 B make conjectures about angles, lines, polygons, circles, and threedimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. Other TEKS that focus on prerequisite knowledge: Mathematics, Grade B identify relationships involving angles in triangles and quadrilaterals Mathematics, Grade B use properties to classify triangles and quadrilaterals. 7.9 A estimate measurements and solve application problems involving length (including perimeter and circumference) and area of polygons and other shapes Geometry G.5 B use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles. G.7 B use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons. G.8 A find areas of regular polygons, circles, and composite figures. G.9 A formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models. G.9 B formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models. TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 13
14 TEKS Objective: Lesson Objectives Geometry G2.B make conjectures about angles, lines, polygons, circles, and threedimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. Content Objectives Students will derive and connect the formulas for the area of parallelograms and for trapezoids. Students will examine how their thinking and perspective can be expressed in mathematical statements such as formulas. Language Objectives Students will be able to use mathematical vocabulary to explain orally, through models, and in writing the attributes of trapezoids and parallelograms, in addition to foundational concepts such as parallel lines. Using solid models of trapezoids and parallelograms, students will work in cooperative groups to discuss and construct area formulas for those two polygons. Students will communicate their findings to the whole group and justify/prove why their discovery is valid. TEXAS COMPREHENSIVE CENTER at the Southwest Educational Development Laboratory 14
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 informationChapter 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 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 informationCoordinate Coplanar Distance Formula Midpoint Formula
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
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 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 informationGeometry Essential Curriculum
Geometry Essential Curriculum Unit I: Fundamental Concepts and Patterns in Geometry Goal: The student will demonstrate the ability to use the fundamental concepts of geometry including the definitions
More informationContent Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade
Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources
More informationObjectives. Cabri Jr. Tools
Activity 24 Angle Bisectors and Medians of Quadrilaterals Objectives To investigate the properties of quadrilaterals formed by angle bisectors of a given quadrilateral To investigate the properties of
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 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 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 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 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 informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 17 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationDistance, Midpoint, and Pythagorean Theorem
Geometry, Quarter 1, Unit 1.1 Distance, Midpoint, and Pythagorean Theorem Overview Number of instructional days: 8 (1 day = 45 minutes) Content to be learned Find distance and midpoint. (2 days) Identify
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 informationGeometry. Unit 6. Quadrilaterals. Unit 6
Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections
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 informationMiddle Grades Mathematics 5 9
Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from realworld situations. 2. Apply problemsolving strategies
More information10.1: Areas of Parallelograms and Triangles
10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a
More information*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.
Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review
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 informationCOURSE OVERVIEW. PearsonSchool.com Copyright 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved
COURSE OVERVIEW The geometry course is centered on the beliefs that The ability to construct a valid argument is the basis of logical communication, in both mathematics and the realworld. There is a need
More informationChapters 4 and 5 Notes: Quadrilaterals and Similar Triangles
Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles IMPORTANT TERMS AND DEFINITIONS parallelogram rectangle square rhombus A quadrilateral is a polygon that has four sides. A parallelogram is
More informationWallingford Public Schools  HIGH SCHOOL COURSE OUTLINE
Wallingford Public Schools  HIGH SCHOOL COURSE OUTLINE Course Title: Geometry Course Number: A 1223, G1224 Department: Mathematics Grade(s): 1011 Level(s): Academic and General Objectives that have an
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 informationName Geometry Exam Review #1: Constructions and Vocab
Name Geometry Exam Review #1: Constructions and Vocab Copy an angle: 1. Place your compass on A, make any arc. Label the intersections of the arc and the sides of the angle B and C. 2. Compass on A, make
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 informationBASIC GEOMETRY GLOSSARY
BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that
More informationGeometry and Spatial Reasoning
Mathematics TEKS Refinement 2006 68 Tarleton State University Geometry and Spatial Reasoning Activity: TEKS: Creating Venn Diagrams with Quadrilaterals (6.6) Geometry and spatial reasoning. The student
More informationAlgebra 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 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 informationGeometry Performance Level Descriptors
Geometry Performance Level Descriptors Limited A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Geometry. A student at this level has an emerging
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 informationOverview Mathematical Practices Congruence
Overview Mathematical Practices Congruence 1. Make sense of problems and persevere in Experiment with transformations in the plane. solving them. Understand congruence in terms of rigid motions. 2. Reason
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 informationFeatured Mathematical Practice: MP.5. Use appropriate tools strategically. MP.6. Attend to precision.
Domain: Geometry 4.G Mathematical Content Standard: 1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures.
More informationModel area formulas for parallelograms, trapezoids, and triangles.
Answers Teacher Copy Lesson 233 Area of Triangles, Trapezoids, and Polygons Learning Targets p. 297 Model area formulas for parallelograms, trapezoids, and triangles. Write equations that represent problems
More information56 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 informationLesson 28: Properties of Parallelograms
Student Outcomes Students complete proofs that incorporate properties of parallelograms. Lesson Notes Throughout this module, we have seen the theme of building new facts with the use of established ones.
More informationLine. A straight path that continues forever in both directions.
Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A
More information100 Math Facts 6 th Grade
100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer
More informationGeometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3
Geometry Concepts Figures that lie in a plane are called plane figures. These are all plane figures. Polygon No. of Sides Drawing Triangle 3 A polygon is a plane closed figure determined by three or more
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 informationMATHEMATICS GRADE LEVEL VOCABULARY DRAWN FROM SBAC ITEM SPECIFICATIONS VERSION 1.1 JUNE 18, 2014
VERSION 1.1 JUNE 18, 2014 MATHEMATICS GRADE LEVEL VOCABULARY DRAWN FROM SBAC ITEM SPECIFICATIONS PRESENTED BY: WASHINGTON STATE REGIONAL MATH COORDINATORS Smarter Balanced Vocabulary  From SBAC test/item
More informationTABLE OF CONTENTS. Free resource from Commercial redistribution prohibited. Understanding Geometry Table of Contents
Understanding Geometry Table of Contents TABLE OF CONTENTS Why Use This Book...ii Teaching Suggestions...vi About the Author...vi Student Introduction...vii Dedication...viii Chapter 1 Fundamentals of
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 informationCK12 Geometry: Midpoints and Bisectors
CK12 Geometry: Midpoints and Bisectors Learning Objectives Identify the midpoint of line segments. Identify the bisector of a line segment. Understand and the Angle Bisector Postulate. Review Queue Answer
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 informationTexas Assessment of Knowledge and Skills (TAKS) 6th Grade
Texas Assessment of Knowledge and Skills (TAKS) 6th Grade 98 99 100 Grade 6 Mathematics TAKS Objectives and TEKS Student Expectations TAKS Objective 1 The student will demonstrate an understanding of numbers,
More informationAssessment Anchors and Eligible Content
M07.AN The Number System M07.AN.1 M07.AN.1.1 DESCRIPTOR Assessment Anchors and Eligible Content Aligned to the Grade 7 Pennsylvania Core Standards Reporting Category Apply and extend previous understandings
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 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 informationGeometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.
Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know
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 informationGeometry Unit 1. Basics of Geometry
Geometry Unit 1 Basics of Geometry Using inductive reasoning  Looking for patterns and making conjectures is part of a process called inductive reasoning Conjecture an unproven statement that is based
More information10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warmup
10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres 10.4 Day 1 Warmup 1. Which identifies the figure? A rectangular pyramid B rectangular prism C cube D square pyramid 3. A polyhedron
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 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 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 informationSu.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)
MA.912.G.2 Geometry: Standard 2: Polygons  Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures
More informationof one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
2901 Clint Moore Road #319, Boca Raton, FL 33496 Office: (561) 4592058 Mobile: (949) 5108153 Email: HappyFunMathTutor@gmail.com www.happyfunmathtutor.com GEOMETRY THEORUMS AND POSTULATES GEOMETRY POSTULATES:
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 informationWinter 2016 Math 213 Final Exam. Points Possible. Subtotal 100. Total 100
Winter 2016 Math 213 Final Exam Name Instructions: Show ALL work. Simplify wherever possible. Clearly indicate your final answer. Problem Number Points Possible Score 1 25 2 25 3 25 4 25 Subtotal 100 Extra
More information2006 ACTM STATE GEOMETRY EXAM
2006 TM STT GOMTRY XM In each of the following you are to choose the best (most correct) answer and mark the corresponding letter on the answer sheet provided. The figures are not necessarily drawn to
More informationAlabama Course of Study Mathematics Geometry
A Correlation of Prentice Hall to the Alabama Course of Study Mathematics Prentice Hall, Correlated to the Alabama Course of Study Mathematics  GEOMETRY CONGRUENCE Experiment with transformations in the
More informationINDEX. Arc Addition Postulate,
# 3060 right triangle, 441442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent
More informationLesson 13: Proofs in Geometry
211 Lesson 13: Proofs in Geometry Beginning with this lesson and continuing for the next few lessons, we will explore the role of proofs and counterexamples in geometry. To begin, recall the Pythagorean
More informationSection 2.1 Rectangular Coordinate Systems
P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is
More informationAngles 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 informationFCAT Math Vocabulary
FCAT Math Vocabulary The terms defined in this glossary pertain to the Sunshine State Standards in mathematics for grades 3 5 and the content assessed on FCAT in mathematics. acute angle an angle that
More information(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units
1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units
More informationLesson 4.4 Congruence shortcuts SSS, AAS, SAS (not AAA or ASS)
Review Problems Lesson 1.3 Terminology Lesson 1.4 Polygons Lesson 1.5 Triangles and special quadrilaterals Lesson 2.5 Angle relationships Lesson 2.6 Special angels on parallel lines Chapter 3 Points of
More informationChapters 6 and 7 Notes: Circles, Locus and Concurrence
Chapters 6 and 7 Notes: Circles, Locus and Concurrence 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
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 informationGeorgia Standards of Excellence Curriculum Map. Mathematics. GSE Geometry
Georgia Standards of Excellence Curriculum Map Mathematics GSE Geometry These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Georgia Department
More informationLEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.
Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the
More information#2. Isosceles Triangle Theorem says that If a triangle is isosceles, then its BASE ANGLES are congruent.
1 Geometry Proofs Reference Sheet Here are some of the properties that we might use in our proofs today: #1. Definition of Isosceles Triangle says that If a triangle is isosceles then TWO or more sides
More informationWORK SCHEDULE: MATHEMATICS 2007
, K WORK SCHEDULE: MATHEMATICS 00 GRADE MODULE TERM... LO NUMBERS, OPERATIONS AND RELATIONSHIPS able to recognise, represent numbers and their relationships, and to count, estimate, calculate and check
More informationGeometry. Unit 1. Transforming and Congruence. Suggested Time Frame 1 st Six Weeks 22 Days
Geometry Unit 1 Transforming and Congruence Title Suggested Time Frame 1 st Six Weeks 22 Days Big Ideas/Enduring Understandings Module 1 Tools of geometry can be used to solve realworld problems. Variety
More informationCONJECTURES  Discovering Geometry. Chapter 2
CONJECTURES  Discovering Geometry Chapter C1 Linear Pair Conjecture  If two angles form a linear pair, then the measures of the angles add up to 180. C Vertical Angles Conjecture  If two angles are
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 informationPreAlgebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio PreAlgebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
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 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 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 informationHonors Geometry Final Exam Study Guide
20112012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.
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 information**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.
Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:
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 informationSixth Grade Math Pacing Guide Page County Public Schools MATH 6/7 1st Nine Weeks: Days Unit: Decimals B
Sixth Grade Math Pacing Guide MATH 6/7 1 st Nine Weeks: Unit: Decimals 6.4 Compare and order whole numbers and decimals using concrete materials, drawings, pictures and mathematical symbols. 6.6B Find
More informationUpper Elementary Geometry
Upper Elementary Geometry Geometry Task Cards Answer Key The unlicensed photocopying, reproduction, display, or projection of the material, contained or accompanying this publication, is expressly prohibited
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 informationSurface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry
Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel
More informationProperties of Special Parallelograms
Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a parallelogram, a rectangle, a square, and a rhombus. Students then
More informationFinal Review Problems Geometry AC Name
Final Review Problems Geometry Name SI GEOMETRY N TRINGLES 1. The measure of the angles of a triangle are x, 2x+6 and 3x6. Find the measure of the angles. State the theorem(s) that support your equation.
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 informationYear 8  Maths Autumn Term
Year 8  Maths Autumn Term Whole Numbers and Decimals Order, add and subtract negative numbers. Recognise and use multiples and factors. Use divisibility tests. Recognise prime numbers. Find square numbers
More informationE XPLORING QUADRILATERALS
E XPLORING QUADRILATERALS E 1 Geometry State Goal 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. Statement of Purpose: The activities in this
More information