The Perpendicular Bisector of a Segment


 Edwin Wood
 2 years ago
 Views:
Transcription
1 Check off the steps as you complete them: The Perpendicular Bisector of a Segment Open a Geometry window in Geogebra. Use the segment tool of draw AB. Under the point tool, select Midpoint of Center, and create the midpoint of AB. (This should be point C.) Select the perpendicular line tool, and click on point C and AB. Use the point tool to make point D anywhere on the perpendicular line. Your diagram should look something like the one at right. Select Distance or Length (in the Angle menu), and measure the distances from D to A and from D to B by clicking on the points. Drag point D anywhere along the line, and observe the measurements DA and DB. 1. What do you notice about DA and DB? 2. DC is called the perpendicular bisector of AB because it is perpendicular to AB and passes through the midpoint of AB. Complete this statement: Any point on the perpendicular bisector of a segment is: 1
2 Follow the directions to find the equation of the perpendicular bisector of the line segment through the given points. 3. Points: 2,6 and 2, 4 a. Graph the segment with endpoints 2,6 2, 4. and b. Find the midpoint of the segment. c. Find the slope of the segment. d. Find the slope of a line perpendicular to this segment. e. Use slopeintercept form y mx b or pointslope form y k m x h, as appropriate to find the equation of a line with slope from part (d) and point from part (b). f. Graph the perpendicular bisector. 2
3 Follow the directions to find the equation of the perpendicular bisector of the line segment through the given points. 4. Points: 1, 6 and 4,3 a. Graph the segment with endpoints 1, 6 4,3. and b. Find the midpoint of the segment. c. Find the slope of the segment. d. Find the slope of a line perpendicular to this segment. e. Use slopeintercept form y mx b or pointslope form y k m x h, as appropriate to find the equation of a line with slope from part (d) and point from part (b). f. Graph the perpendicular bisector. 3
4 ASSIGNMENT 2M Follow the directions to find the equation of the perpendicular bisector of the line segment through the given points. 1. Points: 4,7 and 1, 3 a. Graph the segment with endpoints 4,7 and 1, 3. b. Find the midpoint of the segment. c. Find the slope of the segment. d. Find the slope of a line perpendicular to this segment. e. Use slopeintercept form y mx b equation of the perpendicular bisector. or pointslope form y k m x h, as appropriate to find the f. Graph the perpendicular bisector. 4
5 Follow the directions to find the equation of the perpendicular bisector of the line segment through the given points. 2. Points: 2,5 and 4,1 a. Graph the segment with endpoints 2,5 and 4,1. b. Find the midpoint of the segment. c. Find the slope of the segment. d. Find the slope of a line perpendicular to this segment. e. Use slopeintercept form y mx b equation of the perpendicular bisector. or pointslope form y k m x h, as appropriate to find the f. Graph the perpendicular bisector. 5
6 Follow the directions for each: 1. Points: 4, 2 and 8,4 M2 GEOMETRY PACKET 5 FOR UNIT 2 SECTION 36 & TEST REVIEW Practice for Section 36 a. Graph the segment with endpoints 4, 2 and 8,4. b. Find the midpoint of the segment. c. Find the slope of the segment. d. Find the slope of a line perpendicular to this segment. e. Find the equation of the perpendicular bisector. f. Graph the perpendicular bisector. g. Use algebra to rewrite your equation from part (e) in slopeintercept form y mx b. h. Use algebra to rewrite your equation from part (g) in standard form (x and y on the left side, no decimals or fractions). 6
7 2. Points: 4,6 and 6,2 M2 GEOMETRY PACKET 5 FOR UNIT 2 SECTION 36 & TEST REVIEW a. Graph the segment with endpoints 4,6 and 6,2. b. Find the midpoint of the segment. c. Find the slope of the segment. d. Find the slope of a line perpendicular to this segment. e. Find the equation of the perpendicular bisector. f. Graph the perpendicular bisector. g. Use algebra to rewrite your equation from part (e) in slopeintercept form y mx b. h. Use algebra to rewrite your equation from part (g) in standard form (x and y on the left side, no decimals or fractions). 7
8 Review of 33 to 36 Figures in this review may not be drawn to scale. Multiple Choice: 1. In the diagram at right, TY MV, and m HRY 100. Which of the following statements does not have to be true? (A) m FHM 100 (B) m MHR 80 (C) TRS and FHM are alternate exterior angles (D) YRS and VHR are alternate interior angles 2. In the diagram at right, which statement is the reason that m PIR m YMS? When two parallel lines are cut by a transversal, then (A) Alternate exterior angles are congruent (B) Alternate interior angles are congruent (C) Consecutive interior angles are supplementary (D) Corresponding angles are congruent 3. In the diagram at right, 2 3. Which of the following must be true? (A) r t (B) m 8 m 6 (C) m 4 m 6 (D) m 5 m 3 4. In the diagram at right, m 6 m Which of the following does not have to be true? (A) m 1 m (B) m 5 m (C) r s (D) m 2 m 7 8
9 5. Annie wanted to solve for x, so she set up the equation 5x 2 3x What is her reason? If two parallel lines are cut by a transversal, then (A) Linear pairs are supplementary (B) Corresponding angles are supplementary (C) Alternate interior anlges are congruent (D) Consecutive interior angles are supplementary 6. To solve for x in the diagram at right, Ben used the equation 9x 5 10x 5. The reason that justifies Ben s equation is: If two parallel lines are cut by a transversal, then (A) Alternate interior angles are congruent (B) Alternate exterior angles are congruent (C) Corresponding angles are congruent (D) Consecutive interior angles are supplementary 7. Complete the proof: Given: m n, r s, m Prove: m 3 50 Statements Reasons Corresponding s are 3. m s have = measures 4. m 2 m m
10 8. Complete the proof: Given: 1 2, m 3 88 Prove: m 4 92 M2 GEOMETRY PACKET 5 FOR UNIT 2 SECTION 36 & TEST REVIEW Statements Reasons c d m 3 m Substitution Subtraction Find the slope of each line Find the slopes of PQ and RS, and determine whether the lines are parallel, perpendicular, or neither. 13. P 1,0, Q 5,3, R 6, 1, S 0,2 14. P 5,1, Q 1, 1, R 2,1, S 3, 2 10
11 Graph each line, and write its equation. M2 GEOMETRY PACKET 5 FOR UNIT 2 SECTION 36 & TEST REVIEW 15. the horizontal line through 3,1 16. the line with slope passing through 1, Equation: Equation: 17. the line through 1, 3 and 2,4 18. the line with xintercept 2 and yintercept 1 Equation: Equation: 11
12 Graph each line y 3 x 1 4 y x 2 3 Find the slope of each line. x 21. y x 2y y 4 x (a) Graph MN with M 2,1 and 2,4 N. (b) Graph line parallel to MN with yintercept 4. (c) Write an equation for line. (d) Graph line k perpendicular to MN and passing through 1, 2. (e) Write an equation for line k. 12
13 25. Write an equation of the line through the point 4,5 and parallel to the line 2x y Write an equation of the line through the point 3, 1 and perpendicular to x 3y (a) Graph AB with A 1, 5 and 3,5 B. (b) Find the midpoint of AB. (c) Find the slope of AB. (d) Find the slope of a line perpendicular to AB. (e) Find an equation of the perpendicular bisector of AB in pointslope form. (f) Use algebra to rewrite your equation from (e) in slopeintercept form. (g) Use algebra to rewrite your equation from (g) in standard form. 13
14 28. (a) Graph AB with A 5,2 and 1,4 M2 GEOMETRY PACKET 5 FOR UNIT 2 SECTION 36 & TEST REVIEW B. (b) Find the midpoint of AB. (c) Find the slope of AB. (d) Find the slope of a line perpendicular to AB. (e) Find an equation of the perpendicular bisector of AB in pointslope form. (f) Use algebra to rewrite your equation from (e) in slopeintercept form. (g) Use algebra to rewrite your equation from (g) in standard form. 14
15 29. (a) Graph AB with A 6,0 and 4, 5 B. (b) Find the midpoint of AB. (c) Find the slope of AB. (d) Find the slope of a line perpendicular to AB. (e) Find an equation of the perpendicular bisector of AB in pointslope form. (f) Use algebra to rewrite your equation from (e) in slopeintercept form. (g) Use algebra to rewrite your equation from (g) in standard form. 15
16 30. (a) Graph AB with A 7,1 and 3,5 M2 GEOMETRY PACKET 5 FOR UNIT 2 SECTION 36 & TEST REVIEW B. (b) Find the midpoint of AB. (c) Find the slope of AB. (d) Find the slope of a line perpendicular to AB. (e) Find an equation of the perpendicular bisector of AB in pointslope form. (f) Use algebra to rewrite your equation from (e) in slopeintercept form. (g) Use algebra to rewrite your equation from (g) in standard form. 16
Chapter 4.1 Parallel Lines and Planes
Chapter 4.1 Parallel Lines and Planes Expand on our definition of parallel lines Introduce the idea of parallel planes. What do we recall about parallel lines? In geometry, we have to be concerned about
More informationWarm Up. Write an equation given the slope and yintercept. Write an equation of the line shown.
Warm Up Write an equation given the slope and yintercept Write an equation of the line shown. EXAMPLE 1 Write an equation given the slope and yintercept From the graph, you can see that the slope is
More informationSlopeIntercept Equation. Example
1.4 Equations of Lines and Modeling Find the slope and the y intercept of a line given the equation y = mx + b, or f(x) = mx + b. Graph a linear equation using the slope and the yintercept. Determine
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 informationSection 1.10 Lines. The Slope of a Line
Section 1.10 Lines The Slope of a Line EXAMPLE: Find the slope of the line that passes through the points P(2,1) and Q(8,5). = 5 1 8 2 = 4 6 = 2 1 EXAMPLE: Find the slope of the line that passes through
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 informationMath 10  Unit 7 Final Review  Coordinate Geometry
Class: Date: Math 10  Unit Final Review  Coordinate Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the slope of this line segment.
More informationWrite the Equation of the Line Review
Connecting Algebra 1 to Advanced Placement* Mathematics A Resource and Strategy Guide Objective: Students will be assessed on their ability to write the equation of a line in multiple methods. Connections
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 information51 Perpendicular and Angle Bisectors
51 Perpendicular and Angle Bisectors Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Construct each of the following. 1. A perpendicular bisector. 2. An angle bisector. 3. Find the midpoint and
More informationSlopeIntercept Form of a Linear Equation Examples
SlopeIntercept Form of a Linear Equation Examples. In the figure at the right, AB passes through points A(0, b) and B(x, y). Notice that b is the yintercept of AB. Suppose you want to find an equation
More informationSection summaries. d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2. 1 + y 2. x1 + x 2
Chapter 2 Graphs Section summaries Section 2.1 The Distance and Midpoint Formulas You need to know the distance formula d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 and the midpoint formula ( x1 + x 2, y ) 1 + y 2
More informationUnit 5: Coordinate Geometry Practice Test
Unit 5: Coordinate Geometry Practice Test Math 10 Common Name: Block: Please initial this box to indicate you carefully read over your test and checked your work for simple mistakes. What I can do in this
More informationSolving Equations Involving Parallel and Perpendicular Lines Examples
Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (1,3), (3,3), (2,3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the xcomponent of a point in the form (x,y). Range refers to the set of possible values of the ycomponent of a point in
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 informationExample SECTION 131. XAXIS  the horizontal number line. YAXIS  the vertical number line ORIGIN  the point where the xaxis and yaxis cross
CHAPTER 13 SECTION 131 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants XAXIS  the horizontal
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationAlgebra 1 Chapter 05 Review
Class: Date: Algebra 1 Chapter 05 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Find the slope of the line that passes through the pair of points.
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 informationGeometryUnit 3 Study Guide
Name: Class: Date: GeometryUnit 3 Study Guide Determine the slope of the line that contains the given points. Refer to the figure below. 1 TÊ Á 6, 3 ˆ, V Ê Á 8, 8 ˆ A 2 5 B 5 2 C 0 D 2 5 Solve the system
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 informationGraphing Linear Equations
Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope
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 informationEuclidean Geometry. We start with the idea of an axiomatic system. An axiomatic system has four parts:
Euclidean Geometry Students are often so challenged by the details of Euclidean geometry that they miss the rich structure of the subject. We give an overview of a piece of this structure below. We start
More informationLyman Memorial High School. PreCalculus Prerequisite Packet. Name:
Lyman Memorial High School PreCalculus Prerequisite Packet Name: Dear PreCalculus Students, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry. These
More informationSection 1.1 Linear Equations: Slope and Equations of Lines
Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of
More informationFlorida Algebra 1 EndofCourse Assessment Item Bank, Polk County School District
Benchmark: MA.912.A.2.3; Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Also assesses MA.912.A.2.13; Solve
More information2.3 Writing Equations of Lines
. Writing Equations of Lines In this section ou will learn to use pointslope form to write an equation of a line use slopeintercept form to write an equation of a line graph linear equations using the
More informationChapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.
Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
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 information1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved.
1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points
More informationGRAPHING LINEAR EQUATIONS IN TWO VARIABLES
GRAPHING LINEAR EQUATIONS IN TWO VARIABLES The graphs of linear equations in two variables are straight lines. Linear equations may be written in several forms: SlopeIntercept Form: y = mx+ b In an equation
More information5. Equations of Lines: slope intercept & point slope
5. Equations of Lines: slope intercept & point slope Slope of the line m rise run SlopeIntercept Form m + b m is slope; b is intercept PointSlope Form m( + or m( Slope of parallel lines m m (slopes
More informationGRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points?
GRAPHING (2 weeks) The Rectangular Coordinate System 1. Plot ordered pairs of numbers on the rectangular coordinate system 2. Graph paired data to create a scatter diagram 1. How do you graph points? 2.
More informationGraphing  Parallel and Perpendicular Lines
. Graphing  Parallel and Perpendicular Lines Objective: Identify the equation of a line given a parallel or perpendicular line. There is an interesting connection between the slope of lines that are parallel
More informationSection 1.8 Coordinate Geometry
Section 1.8 Coordinate Geometry The Coordinate Plane Just as points on a line can be identified with real numbers to form the coordinate line, points in a plane can be identified with ordered pairs of
More informationPRIMARY CONTENT MODULE Algebra I Linear Equations & Inequalities T71. Applications. F = mc + b.
PRIMARY CONTENT MODULE Algebra I Linear Equations & Inequalities T71 Applications The formula y = mx + b sometimes appears with different symbols. For example, instead of x, we could use the letter C.
More informationUse the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. 1. measures less than By the Exterior Angle Inequality Theorem, the exterior angle ( ) is larger than
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 informationAlgebraic expressions are a combination of numbers and variables. Here are examples of some basic algebraic expressions.
Page 1 of 13 Review of Linear Expressions and Equations Skills involving linear equations can be divided into the following groups: Simplifying algebraic expressions. Linear expressions. Solving linear
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 informationWhat does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
PRIMARY CONTENT MODULE Algebra  Linear Equations & Inequalities T37/H37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of
More informationGEOMETRY  QUARTER 1 BENCHMARK
Name: Class: _ Date: _ GEOMETRY  QUARTER 1 BENCHMARK Multiple Choice Identify the choice that best completes the statement or answers the question. Refer to Figure 1. Figure 1 1. What is another name
More informationThe PointSlope Form
7. The PointSlope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
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 informationSect The SlopeIntercept Form
Concepts # and # Sect.  The SlopeIntercept Form SlopeIntercept Form of a line Recall the following definition from the beginning of the chapter: Let a, b, and c be real numbers where a and b are not
More informationA synonym is a word that has the same or almost the same definition of
SlopeIntercept Form Determining the Rate of Change and yintercept Learning Goals In this lesson, you will: Graph lines using the slope and yintercept. Calculate the yintercept of a line when given
More informationBrunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year.
Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year. Goal The goal of the summer math program is to help students
More informationLesson 19: Equations for Tangent Lines to Circles
Student Outcomes Given a circle, students find the equations of two lines tangent to the circle with specified slopes. Given a circle and a point outside the circle, students find the equation of the line
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 informationWARM UP EXERCSE. 13 Linear Functions & Straight lines
WARM UP EXERCSE A company makes and sells inline skates. The pricedemand function is p (x) = 190 0.013(x 10) 2. Describe how the graph of function p can be obtained from one of the library functions.
More informationA geometric construction is a drawing of geometric shapes using a compass and a straightedge.
Geometric Construction Notes A geometric construction is a drawing of geometric shapes using a compass and a straightedge. When performing a geometric construction, only a compass (with a pencil) and a
More information34 Equations of Lines
34 Equations of Lines Write an equation in slopeintercept form of the line having the given slope and yintercept. Then graph the 1.m: 4, yintercept: 3 2. yintercept: 1 The slopeintercept form of
More informationLesson 10.1 Skills Practice
Lesson 0. Skills Practice Name_Date Location, Location, Location! Line Relationships Vocabulary Write the term or terms from the box that best complete each statement. intersecting lines perpendicular
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 information2.1. Inductive Reasoning EXAMPLE A
CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers
More informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More information2. Simplify. College Algebra Student SelfAssessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses
College Algebra Student SelfAssessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2
More informationHIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE:  Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
More informationA summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:
summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of midpoint and segment bisector M If a line intersects another line segment
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 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 informationHow Do You Measure a Triangle? Examples
How Do You Measure a Triangle? Examples 1. A triangle is a threesided polygon. A polygon is a closed figure in a plane that is made up of segments called sides that intersect only at their endpoints,
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 informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
More informationWriting the Equation of a Line in SlopeIntercept Form
Writing the Equation of a Line in SlopeIntercept Form SlopeIntercept Form y = mx + b Example 1: Give the equation of the line in slopeintercept form a. With yintercept (0, 2) and slope 9 b. Passing
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 informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
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 informationThe Distance from a Point to a Line
: Student Outcomes Students are able to derive a distance formula and apply it. Lesson Notes In this lesson, students review the distance formula, the criteria for perpendicularity, and the creation of
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 informationWorksheet A5: Slope Intercept Form
Name Date Worksheet A5: Slope Intercept Form Find the Slope of each line below 1 3 Y           Graph the lines containing the point below, then find their slopes from counting on the graph!.
More informationAlgebra 2 PreAP. Name Period
Algebra 2 PreAP Name Period IMPORTANT INSTRUCTIONS FOR STUDENTS!!! We understand that students come to Algebra II with different strengths and needs. For this reason, students have options for completing
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 information1 You Try. 2 You Try.
1 Simplify. 1 You Try. 1) Simplify. AF 1.2 2 Evaluate if, and. 2 You Try. 2) Evaluate if. 1.0 Page 1 of 19 MDC@ACOE (AUSD) 09/13/10 3 Simplify. 3 You Try. 3) Simplify. NS 1.2 4 Simplify. 4 You Try. 4)
More informationDetermining Angle Measure with Parallel Lines Examples
Determining Angle Measure with Parallel Lines Examples 1. Using the figure at the right, review with students the following angles: corresponding, alternate interior, alternate exterior and consecutive
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 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 informationUnit 1: Integers and Fractions
Unit 1: Integers and Fractions No Calculators!!! Order Pages (All in CC7 Vol. 1) 31 Integers & Absolute Value 191194, 203206, 195198, 207210 32 Add Integers 33 Subtract Integers 215222 34 Multiply
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 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 informationTangent line of a circle can be determined once the tangent point or the slope of the line is known.
Worksheet 7: Tangent Line of a Circle Name: Date: Tangent line of a circle can be determined once the tangent point or the slope of the line is known. Straight line: an overview General form : Ax + By
More informationGEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!
GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and
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 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 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 informationI. Model Problems. II. Practice III. Challenge Problems VI. Answer Key
www.mathworksheetsgo.com On Twitter: twitter.com/mathprintables I. Model Problems. II. Practice III. Challenge Problems VI. Answer Key Web Resources Equations of Lines www.mathwarehouse.com/algebra/linear_equation/equationofalineformula.php
More informationMathematics Placement
Mathematics Placement The ACT COMPASS math test is a selfadaptive test, which potentially tests students within four different levels of math including prealgebra, algebra, college algebra, and trigonometry.
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 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 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 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 informationMATH 65 NOTEBOOK CERTIFICATIONS
MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1
More informationMATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationSlopes and Equations of Lines with GeoGebra
Student Name(s): Introduction Today you are going to review how to calculate the slope of a line using 2 different methods. Then you will access the Internet and use a software tool for Geometry and Algebra
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 informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More information