Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.


 Fay Jordan
 2 years ago
 Views:
Transcription
1 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. Opposite rays are two rays that are part of the same line and share the same endpoint. XY and XZ are opposite rays. The figure formed by opposite rays is called a straight angle. Y X Z An angle is the figure formed when two rays share a common endpoint. Two parts are identified on an angle. The common endpoint is called the vertex and the two rays are called the sides. R side vertex S side T
2 Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. We can now give a formal definition for an angle. Definition of an Angle: An angle is a figure formed by two noncollinear rays that have a common endpoint. An angle can be named many ways. S 2 R RST TSR S 2 interior T Notice that the vertex letter is the middle letter in the first two names. exterior Be careful of naming angles by the vertex only if two or more angles share the same vertex. Bookwork: page 93; problems 926
3 Chapter 3.2 Angle Measure Learn how to measure and classify angles. In geometry angles are measured in units called degrees. Postulate 31 Angle Measure Postulate: For every angle, there is a unique positive number between 0 and 180 called the degree measure of the angle. The symbol for degree is m ABC = n and 0 < n < 180 A protractor can be used to measure and draw angles of a certain measure. Postulate 32 Protractor Postulate: On a plane, given AB and a number r between 0 and 180, there is exactly one ray with endpoint A extending on each side of AB such that the degree measure of the angle is r. r r A B This is stating that for any degree measure r, there are only two rays, one on each side of AB, that can create an angle that measures r.
4 Chapter 3.2 Angle Measure Learn how to measure and classify angles. Once the measure of an angle is known, it can be classified based on that measure. Right Angle: A right angle is an angle with a measure of 90 degrees. Acute Angle: An acute angle is an angle with a measure less than 90 degrees. Obtuse Angle: An obtuse angle is an angle with a measure greater than 90 degrees. Drawing Congruent Angles HandsOn Geometry page 99 Bookwork: page 100; problems
5 Magical Midpoints The midpoints of a triangle, when connected, create four congruent triangles. The outer triangles of a quadrilateral, when connected inside the midpoint quadrilateral, create a congruent quadrilateral. See Chapter 3 Investigation on page 102.
6 Chapter 3.3 Angle Addition Postulate Learn that the sum of the measures of two smaller angles equal the measure of the larger angle. R If we draw an angle RST. Draw interior point X. Draw ray SX. This creates angles 1 and 2. S If we measured 1 and 2 and added them together, would their sum equal RST? Postulate 33 Angle Addition Postulate (AA Postulate): For any angle PQR, if A is in the interior of PQR, then m PQA + m AQR = m PQR. 1 2 T X If m 1 + m 2 = m 3, then m 1 = m 3 m 2, and m 2 = m 3 m 1.
7 Chapter 3.3 Angle Addition Postulate Learn that the sum of the measures of two smaller angles equal the measure of the larger angle. You have learned that a line segment has a midpoint that bisects the line segment. Just the same, every angle has a ray that bisects the angle. This ray is called an angle bisector. Definition of an Angle Bisector: The bisector of an angle is the ray with its endpoint at the vertex of the angle, extending into the interior of the angle. The bisector separates the angle into two angles of equal measure.??? This simply states that every angle has a bisector that separates the original angle into two equal angles. Handon Geometry Drawing an angle bisector page 107 Bookwork: page 108; problems
8 Chapter 3.4 Adjacent Angles and Linear Pairs of Angles Identify adjacent angles and linear pairs of angles. When you bisect an angle, you create two angles of equal measure. You also create two angles that share a common side. These angles are called adjacent angles. Definition of Adjacent Angles: Adjacent angles are angles that share a common side and have the same vertex, but have no common interior points in common. If the noncommon side of two adjacent angles form a straight line, then these angles are called a linear pair. Definition of Linear Pair: Two angles form a linear pair if and only if they are adjacent and their noncommon sides are opposite rays. Graphing Calculator Exploration page 112 Bookwork: page 113; problems 822
9 Identify complementary and supplementary angles. Chapter 3.5 Complementary and Supplementary Angles Complementary and Supplementary angles are special sets of angles. Definition of Complementary Angles: Two angles are complementary if and only if the sum of their degree measures is 90. If two angles are complementary, then each is said to be a complement of the other. Complementary angles do not have to share the same vertex or a common side. Meaning, complementary angles do not have to be adjacent. Definition of Supplementary Angles: Two angles are supplementary if and only if the sum of their degree measures is 180. If two angles are supplementary, then each is said to be a supplement of the other. Supplementary angles do not have to share the same vertex or a common side. Meaning, supplementary angles do not have to be adjacent. Postulate 34 Supplement Postulate: If two angles form a linear pair, then they are Bookwork: supplementary. page 120; problems 1331
10 Chapter 3.6 Congruent Angles Identify and use congruent and vertical angles. Recall that congruent segments have the same measure. Congruent angles also have the same measure. Definition of Congruent Angles: Two angles are congruent if and only if they have the same degree measure. When indicating two angles are congruent, an arc is used to show which angles are congruent. m 1 = m 2; When two lines intersect, four angles are formed. There are two pairs of nonadjacent angles. These pairs are called vertical angles and 3 are vertical angles 4 2 and 4 are vertical angles
11 Bookwork: page 126; problems 923 Geometry Chapter 3.6 Congruent Angles Identify and use congruent and vertical angles. Theorem 31 Vertical Angle Theorem: Vertical angles are congruent If two angles are congruent, what do you think is true about their complementary and supplementary angles? Theorem 32: If two angles are congruent, then their complements are also congruent. Theorem 33: If two angles are congruent, then their supplements are also congruent. Theorem 34: If two angles are complementary to the same angle, then they are congruent. Theorem 35: If two angles are supplementary to the same angle, then they are congruent. Theorem 36: If two angles are congruent and supplementary, then each is a right angle. Theorem 37: All right angles are congruent.
12 Chapter 3.7 Perpendicular Lines Identify and use perpendicular lines. Lines that intersect at 90 degrees are perpendicular lines. The square symbol where two lines intersect indicate that the lines are perpendicular. Notice that four right angles are formed from the intersection. Four pairs of adjacent angles are supplementary. These adjacent angles are also linear pairs because they are opposite rays Definition of Perpendicular Lines: Perpendicular lines are lines that intersect to form a right angle. Look at preparing for proof, top of page 129. Theorem 38: If two lines are perpendicular, then they form four right angles.
13 Chapter 3.7 Perpendicular Lines Identify and use perpendicular lines. If we draw a line m. How lines can be drawn that are perpendicular to line m? If we draw a point T on line m, how many lines can be drawn through point T? How many of those lines through point T are perpendicular to line m? Theorem 39: If a line m is in a plane and T is a point on m, then there exists exactly one line in that plane that is perpendicular to m at T. Bookwork: page 132; problems 828.
**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 informationChapter 1. Foundations of Geometry: Points, Lines, and Planes
Chapter 1 Foundations of Geometry: Points, Lines, and Planes Objectives(Goals) Identify and model points, lines, and planes. Identify collinear and coplanar points and intersecting lines and planes in
More informationGeometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment
Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points
More informationTransversals. 1, 3, 5, 7, 9, 11, 13, 15 are all congruent by vertical angles, corresponding angles,
Transversals In the following explanation and drawing, an example of the angles created by two parallel lines and two transversals are shown and explained: 1, 3, 5, 7, 9, 11, 13, 15 are all congruent by
More informationacute angle adjacent angles angle bisector between axiom Vocabulary Flash Cards Chapter 1 (p. 39) Chapter 1 (p. 48) Chapter 1 (p.38) Chapter 1 (p.
Vocabulary Flash ards acute angle adjacent angles hapter 1 (p. 39) hapter 1 (p. 48) angle angle bisector hapter 1 (p.38) hapter 1 (p. 42) axiom between hapter 1 (p. 12) hapter 1 (p. 14) collinear points
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 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 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 informationThe Protractor Postulate and the SAS Axiom. Chapter The Axioms of Plane Geometry
The Protractor Postulate and the SAS Axiom Chapter 3.43.7 The Axioms of Plane Geometry The Protractor Postulate and Angle Measure The Protractor Postulate (p51) defines the measure of an angle (denoted
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 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 informationChapter 6 Notes: Circles
Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment
More 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 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 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 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 informationChapter 5.1 and 5.2 Triangles
Chapter 5.1 and 5.2 Triangles Students will classify triangles. Students will define and use the Angle Sum Theorem. A triangle is formed when three noncollinear points are connected by segments. Each
More informationGeometry Review Flash Cards
point is like a star in the night sky. However, unlike stars, geometric points have no size. Think of them as being so small that they take up zero amount of space. point may be represented by a dot on
More information1.2 Informal Geometry
1.2 Informal Geometry Mathematical System: (xiomatic System) Undefined terms, concepts: Point, line, plane, space Straightness of a line, flatness of a plane point lies in the interior or the exterior
More informationA (straight) line has length but no width or thickness. A line is understood to extend indefinitely to both sides. beginning or end.
Points, Lines, and Planes Point is a position in space. point has no length or width or thickness. point in geometry is represented by a dot. To name a point, we usually use a (capital) letter. (straight)
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 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 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 informationSec 1.1 CC Geometry  Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB.
Sec 1.1 CC Geometry  Constructions Name: 1. [COPY SEGMENT] Construct a segment with an endpoint of C and congruent to the segment AB. A B C **Using a ruler measure the two lengths to make sure they have
More informationGeometry: 11 Day 1 Points, Lines and Planes
Geometry: 11 Day 1 Points, Lines and Planes What are the Undefined Terms? The Undefined Terms are: What is a Point? How is a point named? Example: What is a Line? A line is named two ways. What are the
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 informationA segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. Perpendicular Bisector Theorem
Perpendicular Bisector Theorem A segment, ray, line, or plane that is perpendicular to a segment at its midpoint is called a perpendicular bisector. Converse of the Perpendicular Bisector Theorem If a
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 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 informationPicture. Right Triangle. Acute Triangle. Obtuse Triangle
Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from
More informationPicture. Right Triangle. Acute Triangle. Obtuse Triangle
Name Perpendicular Bisector of each side of a triangle. Construct the perpendicular bisector of each side of each triangle. Point of Concurrency Circumcenter Picture The circumcenter is equidistant from
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 informationThis is a tentative schedule, date may change. Please be sure to write down homework assignments daily.
Mon Tue Wed Thu Fri Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Introductions, Expectations, Course Outline and Carnegie Review summer packet Topic: (11) Points, Lines, & Planes Topic: (12) Segment Measure Quiz
More informationChapter One. Points, Lines, Planes, and Angles
Chapter One Points, Lines, Planes, and Angles Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately
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 informationA convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.
hapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.
More informationChapter 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 informationGEOMETRY. Chapter 1: Foundations for Geometry. Name: Teacher: Pd:
GEOMETRY Chapter 1: Foundations for Geometry Name: Teacher: Pd: Table of Contents Lesson 1.1: SWBAT: Identify, name, and draw points, lines, segments, rays, and planes. Pgs: 14 Lesson 1.2: SWBAT: Use
More informationThe Next Step. Mathematics Applications for Adults. Book Geometry
The Next Step Mathematics Applications for Adults Book 14018  Geometry OUTLINE Mathematics  Book 14018 Geometry Lines and Angles identify parallel lines and perpendicular lines in a given selection of
More informationChapter Three. Parallel Lines and Planes
Chapter Three Parallel Lines and Planes Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately
More informationChapter 1: Points, Lines, Planes, and Angles
Chapter 1: Points, Lines, Planes, and Angles (page 1) 11: A Game and Some Geometry (page 1) In the figure below, you see five points: A,B,C,D, and E. Use a centimeter ruler to find the requested distances.
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 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 informationGrade 4  Module 4: Angle Measure and Plane Figures
Grade 4  Module 4: Angle Measure and Plane Figures Acute angle (angle with a measure of less than 90 degrees) Angle (union of two different rays sharing a common vertex) Complementary angles (two angles
More informationASSIGNMENTS FOR PART 1 OF UNIT 2 LINES AND ANGLES
ASSIGNMENTS FOR PART 1 OF UNIT 2 LINES AND ANGLES Part 1 of Unit 2 includes sections 14, 15, and 28 from our textbook. Due Number Description Topics 2A 2B 2C p. 4142 # 9, 10, 12, 18, 20 23 all, 43
More informationChapter 1 Basics of Geometry Geometry. For questions 15, draw and label an image to fit the descriptions.
Chapter 1 Basics of Geometry Geometry Name For questions 15, draw and label an image to fit the descriptions. 1. intersecting and Plane P containing but not. 2. Three collinear points A, B, and C such
More informationCRS SKILL LEVEL DESCRIPTION Level 1 ALL students must attain mastery at this level
PPF 501 & PPF 503 LESSON _NOTES Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must attain mastery at this level PPF 501 PPF 503 Level 1 Level 2 MOST students will attain mastery of the focus
More informationIncenter Circumcenter
TRIANGLE: Centers: Incenter Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection of the angle bisectors of the triangle. The radius of incircle is
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 informationABC is the triangle with vertices at points A, B and C
Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry  symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the
More 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 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 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 informationCircle geometry theorems
Circle geometry theorems http://topdrawer.aamt.edu.au/geometricreasoning/bigideas/circlegeometry/angleandchordproperties Theorem Suggested abbreviation Diagram 1. When two circles intersect, the line
More informationThe angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons.
Interior Angles of Polygons The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons. The sum of the measures of the interior angles of a triangle
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 informationIntermediate Math Circles October 10, 2012 Geometry I: Angles
Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,
More informationSelected practice exam solutions (part 5, item 2) (MAT 360)
Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On
More informationTerminology: When one line intersects each of two given lines, we call that line a transversal.
Feb 23 Notes: Definition: Two lines l and m are parallel if they lie in the same plane and do not intersect. Terminology: When one line intersects each of two given lines, we call that line a transversal.
More informationMath 366 Lecture Notes Section 11.1 Basic Notions (of Geometry)
Math 366 Lecture Notes Section. Basic Notions (of Geometry) The fundamental building blocks of geometry are points, lines, and planes. These terms are not formally defined, but are described intuitively.
More information1.1 Identify Points, Lines, and Planes
1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures. Key Vocabulary Undefined terms  These words do not have formal definitions, but there is agreement aboutwhat they mean.
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 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 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 informationMathematics 3301001 Spring 2015 Dr. Alexandra Shlapentokh Guide #3
Mathematics 3301001 Spring 2015 Dr. Alexandra Shlapentokh Guide #3 The problems in bold are the problems for Test #3. As before, you are allowed to use statements above and all postulates in the proofs
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 informationLines, Segments, Rays, and Angles
Line and Angle Review Thursday, July 11, 2013 10:22 PM Lines, Segments, Rays, and Angles Slide Notes Title Lines, Segment, Ray A line goes on forever, so we use an arrow on each side to indicate that.
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 informationCongruence. Set 5: Bisectors, Medians, and Altitudes Instruction. Student Activities Overview and Answer Key
Instruction Goal: To provide opportunities for students to develop concepts and skills related to identifying and constructing angle bisectors, perpendicular bisectors, medians, altitudes, incenters, circumcenters,
More 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 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 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 informationCHAPTER 6 LINES AND ANGLES. 6.1 Introduction
CHAPTER 6 LINES AND ANGLES 6.1 Introduction In Chapter 5, you have studied that a minimum of two points are required to draw a line. You have also studied some axioms and, with the help of these axioms,
More information4. Prove the above theorem. 5. Prove the above theorem. 9. Prove the above corollary. 10. Prove the above theorem.
14 Perpendicularity and Angle Congruence Definition (acute angle, right angle, obtuse angle, supplementary angles, complementary angles) An acute angle is an angle whose measure is less than 90. A right
More information6. Angles. a = AB and b = AC is called the angle BAC.
6. Angles Two rays a and b are called coterminal if they have the same endpoint. If this common endpoint is A, then there must be points B and C such that a = AB and b = AC. The union of the two coterminal
More informationTriangle. A triangle is a geometrical figure. Tri means three. So Triangle is a geometrical figure having 3 angles.
Triangle A triangle is a geometrical figure. Tri means three. So Triangle is a geometrical figure having 3 angles. A triangle is consisting of three line segments linked end to end. As the figure linked
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 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 informationGeometry. Kellenberg Memorial High School
20152016 Geometry Kellenberg Memorial High School Undefined Terms and Basic Definitions 1 Click here for Chapter 1 Student Notes Section 1 Undefined Terms 1.1: Undefined Terms (we accept these as true)
More information3.1. Angle Pairs. What s Your Angle? Angle Pairs. ACTIVITY 3.1 Investigative. Activity Focus Measuring angles Angle pairs
SUGGESTED LEARNING STRATEGIES: Think/Pair/Share, Use Manipulatives Two rays with a common endpoint form an angle. The common endpoint is called the vertex. You can use a protractor to draw and measure
More information73 Parallel and Perpendicular Lines
Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal. 73 Parallel Insert Lesson and Perpendicular Title Here Lines Vocabulary perpendicular lines parallel lines
More informationLine AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint.
Section 8 1 Lines and Angles Point is a specific location in space.. Line is a straight path (infinite number of points). Line Segment is part of a line between TWO points. Ray is part of the line that
More information(in alphabetic order).
DETAILED SOLUTIONS AND CONCEPTS  LINES AND ANGLES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! Definition of a
More informationThe Four Centers of a Triangle. Points of Concurrency. Concurrency of the Medians. Let's Take a Look at the Diagram... October 25, 2010.
Points of Concurrency Concurrent lines are three or more lines that intersect at the same point. The mutual point of intersection is called the point of concurrency. Example: x M w y M is the point of
More informationMath 3372College Geometry
Math 3372College Geometry Yi Wang, Ph.D., Assistant Professor Department of Mathematics Fairmont State University Fairmont, West Virginia Fall, 2004 Fairmont, West Virginia Copyright 2004, Yi Wang Contents
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 informationNCERT. In examples 1 and 2, write the correct answer from the given four options.
MTHEMTIS UNIT 2 GEOMETRY () Main oncepts and Results line segment corresponds to the shortest distance between two points. The line segment joining points and is denoted as or as. ray with initial point
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 informationMath 311 Test III, Spring 2013 (with solutions)
Math 311 Test III, Spring 2013 (with solutions) Dr Holmes April 25, 2013 It is extremely likely that there are mistakes in the solutions given! Please call them to my attention if you find them. This exam
More informationConstructing Perpendicular Bisectors
Page 1 of 5 L E S S O N 3.2 To be successful, the first thing to do is to fall in love with your work. SISTER MARY LAURETTA Constructing Perpendicular Bisectors Each segment has exactly one midpoint. A
More information/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
More information*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.
Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the
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 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 informationTriangle congruence can be proved by: SAS. Identify the congruence theorem or postulate:
Geometry Week 14 sec. 7.1 sec. 7.3 section 7.1 Triangle congruence can be proved by: SAS ASA SSS SAA Identify the congruence theorem or postulate: SAS ASA SAA SAA SSS or SAS SSA* (*There is no SSA theorem.)
More informationStatements Goals Identify and evaluate conditional statements. Identify converses and biconditionals. Drafting, Sports, Geography
36 Conditional Statements Goals Identify and evaluate conditional statements. Identify converses and biconditionals. Applications Drafting, Sports, Geography Do you think each statement is true or false?
More informationChapter 1 Exam. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1.
Name: lass: ate: I: hapter 1 Exam Multiple hoice Identify the choice that best completes the statement or answers the question. 1. bisects, m = (7x 1), and m = (4x + 8). Find m. a. m = c. m = 40 b. m =
More informationPARALLEL LINES CHAPTER
HPTR 9 HPTR TL OF ONTNTS 91 Proving Lines Parallel 92 Properties of Parallel Lines 93 Parallel Lines in the oordinate Plane 94 The Sum of the Measures of the ngles of a Triangle 95 Proving Triangles
More informationGEOMETRY FINAL EXAM REVIEW
GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.
More informationName: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester
Name: Chapter 4 Guided Notes: Congruent Triangles Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester CH. 4 Guided Notes, page 2 4.1 Apply Triangle Sum Properties triangle polygon
More information