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

Save this PDF as:

Size: px
Start display at page:

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

## Transcription

2 HS.G-C.4: (+) Construct a tangent line from a point outside a given circle to the circle. 1. tangent line 1. that a tangent line can be constructed from 2. point a point outside a given circle to the circle. circle 1. construct a tangent line. HS.G-C.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 1. arc length 2. radian measure 3. constant proportionality 4. area of a sector 1. that the length of the arc intercepted by an angle is proportional to the radius. 1. derive the formula for area of a sector. 2. derive the proportionality between arc length and radius..

3 High School - Congruence 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, grids, charts, spreadsheets) 3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning? Essential Vocabulary: angle, circle, perpendicular line, parallel line, and line segment, rotation, reflection, translation, rigid transformation, nonrigid transformation, dilation, rotation, reflection, line of reflection, symmetry, congruence, rigid motion, corresponding parts, rigid motion, triangle, corresponding, biconditional statement, triangle congruence, ASA, SAS, SSS, theorem, vertical angles, transversal, alternate interior angles, corresponding angles, perpendicular bisector, equidistant, triangle, interior angles, base angles, isosceles triangles, midpoint, median of a triangle, parallelogram, diagonal, construction, compass, straightedge, equilateral triangle, square, regular hexagon, circle HS.G-CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 1. angle 2. circle 3. perpendicular line 4. parallel line 5. line segment. 1. that the the undefined notions of point, line, distance along a line, and distance around a circular arc relate to the definitions of angle, circle, perpendicular line, parallel line, and line segment. 1. define angle, circle, perpendicular line, parallel line, and line segment.

4 HS.G-CO.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). CPM Geometry Only 1. transformations, 2. geometry software 3. functions 4. points 5. planes 6. distance 7. angle 8. translation 1. that transformations can be represented using a variety of media. 2. that coordinate points can be transformed as functions. 3. that there is a difference between a rigid and non-rigid transformations. 1. represent transformations in a plane. 2. describe transformations as functions. 3. compare transformations. HS.G-CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. CPM Geometry Only 1. rectangle 2. parallelogram 3. trapezoid 4. regular polygon 5. rotations 6. reflections 1. that symmetry can be describes in rotations and reflections. 1. describe rotations and reflections.

5 HS.G-CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 1. rotations 2. reflections 3. translations 4. angles 5. circles 6. perpendicular lines 7. parallel lines 8. line segments 1. that rigid transformations can be defined using basic geometry terms. 1. define rotations, reflections, and transformations in multiple terms. HS.G-CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Only 1. geometric figure 2. rotation 3. reflection 4. translation 5. transformed figure 6. graph paper 7. tracing paper 8. geometry software 9. sequence 10. transformations 11. figure 1. that a sequence of transformations will carry a given figure onto another. 1. draw multistep transformations. 2. explain the types of transformations. 3. use a variety of methods.

6 HS.G-CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Only 1. congruence 2. rigid motion 3. figures 1. that rigid motion does not change the size or shape of an object. 1. compare figures to determine congruence. 2. use transformations on a single figure to find corresponding parts and congruence. HS.G-CO.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. 1. congruence 2. rigid motions 3. triangle 4. corresponding pairs of sides 5. corresponding pairs of angles 1. that rigid motion does not change the size or shape of an object. 1. show congruence in terms of rigid motion. HS.G-CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. 1. triangle congruence 2. ASA, SAS, SSS 1. that triangles can be proved congruent using ASA, SAS, and SSS. 1. explain the criteria for triangle concgruence.

7 HS.G-CO.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints. 1. theorems 2. lines 3. angles 4. vertical angles 5. transversal 6. parallel lines 7. alternate interior angles 8. corresponding angles 9. perpendicular bisector 10. equidistant 11. segment 12. endpoints 1. that congruence can be used to prove theorems about lines and angles. 1. prove theorems about lines and angles. HS.G-CO.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. 1. theorems 2. triangle 3. interior angles 4. base angles 5. isosceles triangles 6. midpoints 7. median of a triangle 1. that congruence can be used to prove theorems about triangles. 1. prove theorems about triangles.

8 HS.G-CO.11: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. 1. theorems 2. parallelograms 3. opposite sides 4. opposite angles 5. diagonals 1. that congruence can be used to prove theorems about parallelograms. 1. prove theorems about parallelograms. 2. bisect parallelograms. HS.G-CO.12: Make formal geometric constructions, including those representing Montana American Indians, with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines; including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. 1. constructions 2. compass 3. straightedge 4. reflective devices 5. geometric software 1. that geometric constructions can be completed in multiple ways. 1. make geometric constructions. 2. copy segments and angles. 3. bisect segments and angles 4. construct parallel lines.

9 HS.G-CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. 1. equilateral triangle 2. square 3. regular hexagon 4. circle 1. that basic regular polygons can be constructed inscribed in a circle. 1. construct regular polygons.

10 High School Geometric Measurement and Dimension 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, grids, charts, spreadsheets) 3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning? Essential Vocabulary: cylinder, pyramid, cone, Cavalieri s principle, cross-section HS.G-GMD.1: Give an informational argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments. 1. formula 2. circumference 3. circle 4. area 5. volume 6. cylinder 7. pyramid 8. cone 1. that arguments can be given to explain circumference, area and volume formulas for circle, cylinder, pyramid, and cone. 1. give informational arguments (in more than one way) for formulas. HS.G-GMD.2: (+) Give an informal argument using Cavalieri s principle for the formulas for the volume of a sphere and other solid figures. Not in current curriculum 1. Cavalieri s principle 2. formula 3. volume 4. sphere 5. solid figures 1. that Cavalieri s principle can be used for the formulas for volume of a sphere and other solid figures. 2. give an informal arguments for formulas.

11 HS.G-GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* 1. volume 2. cylinder 3. pyramid 4. cone sphere 1. that volume formulas can be used for cylinders, pyramids, cones, and spheres. 1. use formulas to solve problems. HS.G-GMD.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. 1. shapes 2. two-dimensional, 3. three-dimensional 4. cross-sections 5. rotations 1. that 2-D and 3-D objects can be used to identify one another. 1. identify the shapes of two-dimensional cross-sections of three-dimensional objects. 2. identify three-dimensional objects generated by rotations of two-dimensional objects.

12 High School Expressing Geometric Properties with Equations 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, grids, charts, spreadsheets) 3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning? Essential Vocabulary: complete the square, Pythagorean Theorem, parabola, focus, directix, ellipse, hyperbola, foci, slope, parallel, perpendicular, point, line segment, partition, ratio, distance formula, perimeter, area HS.G-GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 1. circle 2. center 3. radius 4. Pythagorean Theorem 5. complete the square 1. that the Pythagorean Theorem can be used to derive the equation of a circle. 1. derive the equation of a circle of given center and radius using the Pythagorean Theorem. 2. find the center and radius of a circle by completing the square. HS.G-GPE.2: Derive the equation of a parabola given a focus and directrix. Algebra III 1. equation 1. that the equation of a parabola can be 2. parabola derived. 3. focus 4. directix 1. derive the equation of a parabola given a focus and directix.

13 HS.G-GPE.3: (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. Algebra III 1. ellipse 2. hyperbola 3. foci 1. that the equation of ellipses and hyperbolas can be derived given the foci. 1. derive the equations of ellipses and hyperbolas given the foci. HS.G-GPE.4: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). 1. coordinates 2. geometric theorems 1. that coordinates can be used to prove simple geometric theorems algebraically. 1. use coordinates to prove theorems algebraically. HS.G-GPE.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). 1. slope, 2. parallel 3. perpendicular 1. that slope criteria can be used to solve geometric problems. 1. prove the slope of parallel and perpendicular lines to use them to solve geometric problems.

14 HS.G-GPE.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 1. point 2. line segment 3. partition 4. ratio 1. that points partition line segments in a given ratio. 1. find a point on a segment that creates a bisector or any other given ratio. HS.G-GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. * 1. coordinates 2. perimeters 3. polygons 4. area of triangle 5. area of rectangle 6. distance formula 1. that coordinates can be used to compute perimeters of polygons and areas of triangles and rectangles. 1. use coordinates to compute perimeters and areas of triangles and rectangles. 2. use the distance formula.

15 High School Modeling with Geometry 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, grids, charts, spreadsheets) 3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning? Essential Vocabulary : geometric shapes, measure, properties, density, area, volume, geometric methods HS.G-MG.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder; modeling a Montana American Indian tipi as a cone).* 1. geometric shapes measures 2. properties 1. that objects can be described using a variety of characteristics. 1. use geometric shapes, their measures, and their properties to describe objects. HS.G-MG.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* 1. density area 2. volume 1. that concepts of density are based on area and volume. 1. apply concepts of density based on area and volume in modeling situations HS.G-MG.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* 1. geometric methods 1. that geometric methods can be used to solve design problems. 1. apply geometric methods to solve design problems.

16 High School Similarity, Right Triangles, and Trigonometry 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, grids, charts, spreadsheets) 3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning? Essential Vocabulary : scale factor, similarity, similarity transformations, proportionality, AA, criterion, Pythagorean Theorem, similarity, side ratios, trigonometric ratios, sine, cosine, complementary angles, trigonometric ratios, auxiliary line, vertex, Law of Sines, Law of Cosines, resultant forces HS.G-SRT.1: 1. Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. 1. properties of dilations 2. center 3. scale factor 1. that a dilation changes a figure s size based on scale factor. 1. verify the properties of dilations. HS.G-SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. 1. similarity 2. similarity transformations 3. proportionality 4. corresponding angles 5. corresponding sides 1. that transformations can be used to decide if two figures are similar. 1. determine if two figures are similar using similarity transformations. 2. explain why two figures are similar using similarity transformations

17 HS.G-SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 1. similarity transformations 2. AA 3. criterion 1. that triangles can be shown to be similar using the AA criterion. 1. use properties of transformations to establish the AA criterion. HS.G-SRT.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. 1. theorems, 2. triangle 3. parallel, 4. Pythagorean Theorem 1. that similarity can be used to complete proofs about triangles. 1. prove theorems about triangles. HS.G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 1. congruence 2. similarity 3. triangles 4. geometric figures 1. that congruence and similarity can be used for triangles to complete proofs about geometric figures. 1. solve problems using congruence and similarity. 2. prove relationships in geometric figures. HS.G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 1. side ratios 2. right triangles 3. trigonometric ratios 4. acute angles 1. that side ratios in right triangles are properties of the angles in the triangle. 1. define trigonometric ratios. 2. explain the relationship between side ratios and trigonometric ratios.

18 HS.G-SRT.7: Explain and use the relationship between the sine and cosine of complementary angles. 1. sine 2. cosine 3. complementary angles 1. that there is a relationship between sine and cosine of complementary angles. 1. explain how sine and cosine are related. HS.G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Geometry Enduring Understanding 1. trigonometric ratios 2. Pythagorean Theorem 1. that the Pythagorean Theorem and trigonometric ratios can be used to solve right triangles. 1. apply trigonometric ratios and the Pythagorean Theorem to right triangle. 2. model trigonometric ratios and the Pythagorean Theorem. HS.G-SRT.9: (+) Derive the formula A = ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Algebra II/Trig 1. area formula 2. auxiliary line 3. vertex 4. perpendicular 5. opposite side 1. that sine can be used to derive the formula of a triangle using sine. 1. derive the formula of a triangle using sine. HS.G-SRT.10: (+) Prove the Laws of Sines and Cosines and use them to solve problems. 1. law of sines 2. law of cosines 1. that the laws of sines and cosines can be used to solve problems. 1. prove the laws of sines and cosines. 2. use the laws to solve problems

19 HS.G-SRT.11: (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Only 1. Law of Sines 2. Law of Cosines 3. measurements 4. resultant forces 1. that the Laws of Sines and Cosines can be used on right and non-right triangles in application based problems. 1. apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

### Overview 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

### 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

### 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,

### 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

### Geometry Math Standards and I Can Statements

Geometry Math Standards and I Can Statements Unit 1 Subsection A CC.9-12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions

### Name 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

### A COURSE OUTLINE FOR GEOMETRY DEVELOPED BY ANN SHANNON & ASSOCIATES FOR THE BILL & MELINDA GATES FOUNDATION

A COURSE OUTLINE FOR GEOMETRY DEVELOPED BY ANN SHANNON & ASSOCIATES FOR THE BILL & MELINDA GATES FOUNDATION JANUARY 2014 Geometry Course Outline Content Area G0 Introduction and Construction G-CO Congruence

### Georgia Standards of Excellence Mathematics

Georgia Standards of Excellence Mathematics Standards GSE Geometry K-12 Mathematics Introduction Georgia Mathematics focuses on actively engaging the student in the development of mathematical understanding

### 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,

### 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

### 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

### Geometry 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

### 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

### 2, 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 014-015 Day Concepts Lesson Benchmark(s) Complexity Level 1 Identify Points, Lines, & Planes 1-1 MAFS.91.G-CO.1.1 1 Use Segments & Congruence, Use Midpoint & 1-/1- MAFS.91.G-CO.1.1,

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 real-world. There is a need

### Curriculum Map by Block Geometry Mapping for Math Block Testing 2007-2008. August 20 to August 24 Review concepts from previous grades.

Curriculum Map by Geometry Mapping for Math Testing 2007-2008 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)

### Centroid: 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:

### 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

### Coordinate 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 two-dimensional coordinate systems to

### Conjectures 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:

### Geometry 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.

### Georgia Standards of Excellence Curriculum Map. Mathematics. GSE Analytic Geometry

Georgia Standards of Excellence Curriculum Map Mathematics GSE Analytic Geometry These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. GSE Analytic

### CONJECTURES - Discovering Geometry. Chapter 2

CONJECTURES - Discovering Geometry Chapter C-1 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

### Geometry Credit Recovery

Geometry Credit Recovery COURSE DESCRIPTION: This is a comprehensive course featuring geometric terms and processes, logic, and problem solving. Topics include parallel line and planes, congruent triangles,

### Content 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

### Topics 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

### Middle Grades Mathematics 5 9

Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from real-world situations. 2. Apply problem-solving strategies

### Level: High School: Geometry. Domain: Expressing Geometric Properties with Equations G-GPE

1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Translate between the geometric

### 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

### BASIC 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

### 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

### 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,

### PUBLIC 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 8-12

### Framework for developing schemes of work for the geometry curriculum for ages 14-16

Framework for developing schemes of work for the geometry curriculum for ages 14-16 CURRICULUM GRADES G - F GRADES E - D GRADES C - B GRADES A A* INVESTIGATION CONTEXT Distinguish Know and use angle, Construct

### Blue Springs School District Geometry - Syllabus 1 Credit Hour

Teacher: Mr. Jakob Estep Plan: 2 nd Hour (8:20-9:10) School Phone Number: (816) 224-1315 Email: jestep@bssd.net Blue Springs School District Geometry - Syllabus 1 Credit Hour 2014-2015 Textbook: Course

### Geometry College Prep C CURRICULUM GUIDE

Geometry College Prep C CURRICULUM GUIDE Number: 313 Level: College Prep C Revised: August, 2012 Textbook: GEOMETRY CONCEPTS AND SKILLS, McDougal Littell, 2003 Credits: 5 Credits Midterm Exam Revised:

# 30-60 right triangle, 441-442, 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

### DRAFT. Geometry EOC Item Specifications

DRAFT Geometry EOC Item Specifications The release of the updated FSA Test Item Specifications is intended to provide greater specificity for item writers in developing items to be field tested in 2016.

### of 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) 459-2058 Mobile: (949) 510-8153 Email: HappyFunMathTutor@gmail.com www.happyfunmathtutor.com GEOMETRY THEORUMS AND POSTULATES GEOMETRY POSTULATES:

### CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide. CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide

Curriculum Map/Pacing Guide page of 6 2 77.5 Unit : Tools of 5 9 Totals Always Include 2 blocks for Review & Test Activity binder, District Google How do you find length, area? 2 What are the basic tools

### Geometry Texas Mathematics: Unpacked Content

Geometry Texas Mathematics: Unpacked Content What is the purpose of this document? To increase student achievement by ensuring educators understand specifically what the new standards mean a student must

### Syllabi of High School Courses According to the Common Core Mathematics Standards

Syllabi of High School Courses According to the Common Core Mathematics Standards H. Wu August 4, 2011 The following are two sets of proposed syllabi for high school mathematics classes. Ever since the

### 3. Lengths and areas associated with the circle including such questions as: (i) What happens to the circumference if the radius length is doubled?

1.06 Circle Connections Plan The first two pages of this document show a suggested sequence of teaching to emphasise the connections between synthetic geometry, co-ordinate geometry (which connects algebra

### Distance, 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

### Su.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

### (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

### Math. MCC9 12.N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the

MCC9 12.N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms

### Higher Geometry Problems

Higher Geometry Problems ( Look up Eucidean Geometry on Wikipedia, and write down the English translation given of each of the first four postulates of Euclid. Rewrite each postulate as a clear statement

### After your registration is complete and your proctor has been approved, you may take the Credit by Examination for GEOM 1B.

GEOM 1B Geometry I, Second Semester #PR-109, BK-1030 (v.3.0) To the Student: After your registration is complete and your proctor has been approved, you may take the Credit by Examination for GEOM 1B.

### Chapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter C. High School

High School 111.C. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter C. High School Statutory Authority: The provisions of this Subchapter C issued under the Texas Education

### 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

### 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

### 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

### 7. 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

### Geometry 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,

### Scope & Sequence MIDDLE SCHOOL

Math in Focus is a registered trademark of Times Publishing Limited. Houghton Mifflin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A. 06/13 MS77941n Scope & Sequence MIDDLE SCHOOL

### Florida Geometry EOC Assessment Study Guide

Florida Geometry EOC Assessment Study Guide The Florida Geometry End of Course Assessment is computer-based. During testing students will have access to the Algebra I/Geometry EOC Assessments Reference

### Wallingford 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): 10-11 Level(s): Academic and General Objectives that have an

### ABC 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

### 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

### Geometry, 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

### Chapters 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

### 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

### 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:

### Chapters 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

### Wentzville School District Curriculum Development Template Stage 1 Desired Results

Wentzville School District Curriculum Development Template Stage 1 Desired Results Integrated Math 8 Unit Four Geometry Unit Title: Geometry Course: Integrated Math 8 Brief Summary of Unit: In this unit

### 0810ge. 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

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

### 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

### 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

### 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

### 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

### The 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

### High School Geometry Test Sampler Math Common Core Sampler Test

High School Geometry Test Sampler Math Common Core Sampler Test Our High School Geometry sampler covers the twenty most common questions that we see targeted for this level. For complete tests and break

### HIGH SCHOOL: GEOMETRY (Page 1 of 4)

HIGH SCHOOL: GEOMETRY (Page 1 of 4) Geometry is a complete college preparatory course of plane and solid geometry. It is recommended that there be a strand of algebra review woven throughout the course

### 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

### CCGPS UNIT 3 Semester 1 ANALYTIC GEOMETRY Page 1 of 32. Circles and Volumes Name:

GPS UNIT 3 Semester 1 NLYTI GEOMETRY Page 1 of 3 ircles and Volumes Name: ate: Understand and apply theorems about circles M9-1.G..1 Prove that all circles are similar. M9-1.G.. Identify and describe relationships

### Geometry: A Common Core Program

1 Tools of Geometry This chapter begins by addressing the building blocks of geometry which are the point, the line, and the plane. Students will construct line segments, midpoints, bisectors, angles,

### MATHEMATICS Grade 6 Standard: Number, Number Sense and Operations

Standard: Number, Number Sense and Operations Number and Number C. Develop meaning for percents including percents greater than 1. Describe what it means to find a specific percent of a number, Systems

Chapter Additional Topics in Math In addition to the questions in Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math, the SAT Math Test includes several questions that are

### A Correlation of Pearson Algebra 1, Geometry, Algebra 2 Common Core 2015

A Correlation of Pearson,, Common Core 2015 To the North Carolina High School Mathematics Alignment to Traditional Text - MATH II A Correlation of Pearson,, Common Core, 2015 Introduction This document

### 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

### NEW 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

### Circle 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

### KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number

KS4 Curriculum Plan Maths FOUNDATION TIER Year 9 Autumn Term 1 Unit 1: Number 1.1 Calculations 1.2 Decimal Numbers 1.3 Place Value Use priority of operations with positive and negative numbers. Simplify

### Lesson 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.

### Students 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?

### Whole Numbers and Integers (44 topics, no due date)

Course Name: PreAlgebra into Algebra Summer Hwk Course Code: GHMKU-KPMR9 ALEKS Course: Pre-Algebra Instructor: Ms. Rhame Course Dates: Begin: 05/30/2015 End: 12/31/2015 Course Content: 302 topics Whole

### 10-4 Inscribed Angles. Find each measure. 1.

Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semi-circle. 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

### 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

### A 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

### Geometry: Euclidean. Through a given external point there is at most one line parallel to a

Geometry: Euclidean MATH 3120, Spring 2016 The proofs of theorems below can be proven using the SMSG postulates and the neutral geometry theorems provided in the previous section. In the SMSG axiom list,

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 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

### Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1

Student Name: Teacher: Date: District: Miami-Dade 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

### Congruence. 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,

### 1) Perpendicular bisector 2) Angle bisector of a line segment

1) Perpendicular bisector 2) ngle bisector of a line segment 3) line parallel to a given line through a point not on the line by copying a corresponding angle. 1 line perpendicular to a given line through

### Unit 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