Geometry Chapter 2: Geometric Reasoning Lesson 1: Using Inductive Reasoning to Make Conjectures Inductive Reasoning:


 Willa Howard
 2 years ago
 Views:
Transcription
1 Geometry Chapter 2: Geometric Reasoning Lesson 1: Using Inductive Reasoning to Make Conjectures Inductive Reasoning: Conjecture: Advantages: can draw conclusions from limited information helps us to organize our thinking human beings know how to use inductive reasoning naturally Disadvantages: sometimes we draw the wrong conclusion from the information our conclusions are only as strong as the evidence that we choose to consideration in mathematics, just one example which contradicts our conclusion tells us that our conclusion is wrong cannot be used to prove something mathematically Ex: #1: Find the next item in each pattern. January, March, May,... 7, 14, 21, 28,... Ex: #2: Complete each conjecture. The sum of two positive numbers is. The quotient of one positive number and one negative number is. The number of lines formed by four points, no three of which are collinear, is. If the side length of a square is doubled, the perimeter of the square is. Ex: #3: Biology Application A biologist observed bluewhale spouts of 25ft, 29ft, 27ft, and 24ft. Another biologist recorded humpbackwhale spouts of 8ft, 7ft, 8ft, and 9ft. Make a conjecture based on the data. Page 1
2 To show that a conjecture is true you must prove it for all possibilities. To show that a conjecture is false you only have to show one counterexample. Counterexample: Examples: Show that each conjecture is false by finding a counterexample. For every integer n, n³ is positive. Two complementary angles are not congruent. Based on the data in Example 4C, the monthly high temperature in Abilene is never below 90 F for two months in a row. Chapter 2 Lesson 2: Conditional Statements Conditional Statement Conditional Statement: Definition Symbols Venn Diagram Hypothesis: Conclusion: Ex: #1 Identify the hypothesis and conclusion of each statement. If today is Thanksgiving Day, then today is A number is a rational number if it is an integer. Thursday. If an angle measures 40º, then it is an acute angle. Ex: #2 Write a conditional statement from each of the following. An obtuse triangle has exactly one obtuse angle. Congruent segments have equal measures. Page 2
3 Birds Blue Jays Adjacent angles Linear pair Truth value: When is a conditional false? Ex: #3 Determine if each conditional is true. If false, give a counterexample. If this month is August, then next month is If two angles are acute, then they are congruent. September. If an even number greater than 2 is prime, then = 8. If a number is odd, then it is divisible by 3. Negation: Chapter 2 Lesson 3: Using Deductive Reasoning to Verify Conjectures Deductive Reasoning: Advantages: proves that a statement is always true follows a systematic pattern of rules Disadvantages: can be difficult to use a skill that can take a lot of practice Ex: #1 Is each conclusion a result of inductive or deductive reasoning? Explain your answer. There is a myth that you can balance an egg on its There is a myth that the Great Wall of China is the end only on the spring equinox. A person was able only manmade object visible from the Moon. The to balance an egg on July 8, September 21, and Great Wall is barely visible in photographs taken December 19. Therefore this myth is false. from 180 miles above the Earth. The moon is about 237,000 miles from the Earth. Therefore the myth cannot be true. Page 3
4 Law of Detachment If p q is a true statement and p is true, then q is true. In your own words: Law of Syllogism If p q and q r are both true statements, then p r is a true statement. In your own words: Ex: #2 Determine if each conjecture is valid by the Law of Detachment. Given: If the side lengths of a triangle are 5cm, Given: In the World Series, if a team wins four 12cm, and 13cm, then the area of the triangle is games, then the team wins the series. The Red Sox 30cm². The area of ΔPQR is 30cm². won four games in the 2004 World Series. Conjecture: The side lengths of ΔPQR are 5cm, Conjecture: The Red Sox won the 2004 World 12, cm, and 13cm. Series. Ex: #3 Determine if each conjecture is valid by the Law of Syllogism. Given: If a figure is a kite, then it is a Given: If a number is divisible by 2, then it is quadrilateral. If a figure is a quadrilateral, then it is even. If a number is even, then it is an integer. a polygon. Conjecture: If a number is an integer, then it is Conjecture: If a figure is a kite, then it is a divisible by 2. polygon. Ex: #4 Draw a conclusion from the given information. Given: If 2y = 4, then z = 1. If x + 3 = 12, Given: If the sum of the measures of two angles is then 2y = º, then the angles are supplementary. If two angles are supplementary, they are not angles of a x + 3 = 12. triangle. m A = 135º, and m B = 45º. Page 4
5 Chapter 2 Lesson 4: Biconditional Statements and Definitions Biconditional: Definition Symbol All mathematical definitions can be written as biconditional statements. An angle is obtuse if and only if its measure is greater than 90º and less than 180º. A figure is circle if and only if it is the set of all points that are the same distance from a given point. When is a biconditional true? Definition: Polygon: Triangle: Quadrilateral: Page 5
6 Chapter 2 Lesson 5: Algebraic Proofs Proof: Algebraic Properties of Equality For any real number a, b, and c: Addition Property Multiplication Property Reflexive Property Symmetric Property Transitive Property Substitution Property Distributive Property The solution to an algebraic equation is a type of proof. The steps must appear in the correct order, and you must be able to justify each step. Ex: #1 Solve the equation and write a justification for each step. 1. 4m 8 = 12 Given Page 6
7 1. n + 8 = 6 5 Given Ex: #3 Write a justification for each step. 4 x  A 3 x + 5 D N NO = NM + MO 2 x M 3 x  O B m A B C = 8 x 6 x C 4x 4 = 2x + (3x 9) 4x 4 = 5x 94 = x 9 5 = x m ABC =m ABD + m DBC 8x = (3x + 5) + (6x 16) 8x = 9x 11 x =  11 x = 11 Properties of Congruence Reflexive Property of Congruence: Symmetric Property of Congruence: Transitive Property of Congruence: Each property of congruence has a corresponding property of equality. Page 7
8 Ex: #4 Identify the property that justifies each statement. If EF = GH and GH = JK, then EF = JK AB = 14 then 14 = AB m EJM = m MJE If 2( x 5 ) = 7, then 2x 10 = 7 AB CD and CD EF, then AB EF QRS QRS Chapter 2 Lesson 6: Geometric Proof Theorem: TwoColumn Proof: Theorem Hypothesis Conclusion Linear Pair Theorem: If two angles form a linear pair, then they are supplementary. Right Angle Congruence Theorem: all right angles are congruent. Ex: #1 Write a justification for each step, given that A and B are supplementary and m A = 45º Statements Reasons A and B are supplementary and m A = 45º m A + m B = m B = 180 m B = 135 Page 8
9 M Ex: #2 Given: N is the midpoint of MP, Q is the midpoint of RP and PQ MN. Prove: PN QR P N Q R Statements Reasons N is the midpoint of MP, Q is the midpoint of RP PQ MN PN MN PQ PN PQ PN QR QR Ex: #3 Fill in the blanks to complete the twocolumn proofs. Given: XY Prove: XY XY Statements Reasons Given XY = XY Def. of congruent segments. Ex: #4 Write a twocolumn proof. Given: 1 and 2 are supplementary and 2 and 3 are supplementary Prove: 1 3 Statements Reasons Page 9
10 E Ex: #5 Given: FD bisects EFC and FC bisects DFB Prove: EFD CFB F B C D Statements Reasons Page 10
11 Chapter 2 Extension: Introduction to Symbolic Logic Compound Statement: Truth Table: Compound Statements Term Words Symbols Example Conjunction Disjunction When is a conjunction true? When is a disjunction true? Examples: Use p, q, and r to write a compound statement, then find its truth value. p: the month after April is May q: the next prime number after 13 is 17 r: half of 19 is 9 p q q r Examples: Construct a truth table for the following compound statements. u v u v u v p q r p q (p q) r Page 11
Geometry  Chapter 2 Review
Name: Class: Date: Geometry  Chapter 2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine if the conjecture is valid by the Law of Syllogism.
More informationVocabulary. Term Page Definition Clarifying Example. biconditional statement. conclusion. conditional statement. conjecture.
CHAPTER Vocabulary The table contains important vocabulary terms from Chapter. As you work through the chapter, fill in the page number, definition, and a clarifying example. biconditional statement conclusion
More informationIn the examples above, you used a process called inductive reasoning to continue the pattern. Inductive reasoning is.
Lesson 7 Inductive ing 1. I CAN understand what inductive reasoning is and its importance in geometry 3. I CAN show that a conditional statement is false by finding a counterexample Can you find the next
More information2.) 5000, 1000, 200, 40, 3.) 1, 12, 123, 1234, 4.) 1, 4, 9, 16, 25, Draw the next figure in the sequence. 5.)
Chapter 2 Geometry Notes 2.1/2.2 Patterns and Inductive Reasoning and Conditional Statements Inductive reasoning: looking at numbers and determining the next one Conjecture: sometimes thought of as an
More informationEx 1: For points A, B, and C, AB = 10, BC = 8, and AC = 5. Make a conjecture and draw a figure to illustrate your conjecture.
Geometry 21 Inductive Reasoning and Conjecturing A. Definitions 1. A conjecture is an guess. 2. Looking at several specific situations to arrive at a is called inductive reasoning. Ex 1: For points A,
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 information14 add 3 to preceding number 35 add 2, then 4, then 6,...
Geometry Definitions, Postulates, and Theorems hapter 2: Reasoning and Proof Section 2.1: Use Inductive Reasoning Standards: 1.0 Students demonstrate understanding by identifying and giving examples of
More information9/10/10. Objectives. Using Inductive Reasoning to. 21 Using Inductive Reasoning to 21. Make Conjectures 21
to Make Conjectures Geometry Warm Up Complete each sentence. 1.? points are points that lie on the same line. Collinear 2.? points are points that lie in the same plane. Coplanar 3. The sum of the measures
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 informationWarm Up Lesson Presentation Lesson Quiz. Holt Geometry
21 Warm Up Lesson Presentation Lesson Quiz Warm Up Complete each sentence. 1.? points are points that lie on the same line. Collinear 2.? points are points that lie in the same plane. Coplanar 3. The
More informationGeometry Chapter 2 Study Guide
Geometry Chapter 2 Study Guide Short Answer ( 2 Points Each) 1. (1 point) Name the Property of Equality that justifies the statement: If g = h, then. 2. (1 point) Name the Property of Congruence that justifies
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 informationPROVING STATEMENTS IN GEOMETRY
CHAPTER PROVING STATEMENTS IN GEOMETRY After proposing 23 definitions, Euclid listed five postulates and five common notions. These definitions, postulates, and common notions provided the foundation for
More informationReasoning and Proof Review Questions
www.ck12.org 1 Reasoning and Proof Review Questions Inductive Reasoning from Patterns 1. What is the next term in the pattern: 1, 4, 9, 16, 25, 36, 49...? (a) 81 (b) 64 (c) 121 (d) 56 2. What is the next
More informationChapter Two. Deductive Reasoning
Chapter Two Deductive Reasoning 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 apply
More informationObjectives. 22 Conditional Statements
Geometry Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90. F 2. All perfectsquare numbers are positive. 3. Every prime number is odd. F 4. Any three
More informationFind the measure of each numbered angle, and name the theorems that justify your work.
Find the measure of each numbered angle, and name the theorems that justify your work. 1. The angles 2 and 3 are complementary, or adjacent angles that form a right angle. So, m 2 + m 3 = 90. Substitute.
More informationGeometry Essential Curriculum
Geometry Essential Curriculum Unit I: Fundamental Concepts and Patterns in Geometry Goal: The student will demonstrate the ability to use the fundamental concepts of geometry including the definitions
More 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 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 information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
More informationShow all work for credit. Attach paper as needed to keep work neat & organized.
Geometry Semester 1 Review Part 2 Name Show all work for credit. Attach paper as needed to keep work neat & organized. Determine the reflectional (# of lines and draw them in) and rotational symmetry (order
More informationState the assumption you would make to start an indirect proof of each statement.
1. State the assumption you would make to start an indirect proof of each statement. Identify the conclusion you wish to prove. The assumption is that this conclusion is false. 2. is a scalene triangle.
More informationGeometry: 2.12.3 Notes
Geometry: 2.12.3 Notes NAME 2.1 Be able to write all types of conditional statements. Date: Define Vocabulary: conditional statement ifthen form hypothesis conclusion negation converse inverse contrapositive
More informationGEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
More informationGeometry Topic 5: Conditional statements and converses page 1 Student Activity Sheet 5.1; use with Overview
Geometry Topic 5: Conditional statements and converses page 1 Student Activity Sheet 5.1; use with Overview 1. REVIEW Complete this geometric proof by writing a reason to justify each statement. Given:
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 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 informationIn the statement, each side is the same "XY = XY". The Reflexive Property justifies this statement.
State the property that justifies each statement. 1. If m 1 = m 2 and m 2 = m 3, then m 1 = m 3. There are two parts to the hypotheses. "If m 1 = m 2 and m 2 = m 3, then m 1 = m 3. "The end of the first
More information41 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240.
ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.
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 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 informationTeacher Annotated Edition Study Notebook
Teacher Annotated Edition Study Notebook Copyright by The McGrawHill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be
More informationAlgebraic Properties and Proofs
Algebraic Properties and Proofs Name You have solved algebraic equations for a couple years now, but now it is time to justify the steps you have practiced and now take without thinking and acting without
More informationThe Polygon AngleSum Theorems
61 The Polygon AngleSum Theorems Common Core State Standards GSRT.B.5 Use congruence... criteria to solve problems and prove relationships in geometric figures. MP 1, MP 3 Objectives To find the sum
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 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 informationCOURSE OVERVIEW. PearsonSchool.com Copyright 2009 Pearson Education, Inc. or its affiliate(s). All rights reserved
COURSE OVERVIEW The geometry course is centered on the beliefs that The ability to construct a valid argument is the basis of logical communication, in both mathematics and the realworld. There is a need
More 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 informationFoundations of Geometry 1: Points, Lines, Segments, Angles
Chapter 3 Foundations of Geometry 1: Points, Lines, Segments, Angles 3.1 An Introduction to Proof Syllogism: The abstract form is: 1. All A is B. 2. X is A 3. X is B Example: Let s think about an example.
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 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. 3. PROOF Write a twocolumn proof to prove that if ABCD is a rhombus with diagonal. 1. If, find. A rhombus is a parallelogram with all
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 information2.5 IfThen Statements and
Page 1 of 6 2.5 IfThen Statements and Deductive Reasoning Goal Use ifthen statements. Apply laws of logic. An ifthen statement has two parts. The if part contains the hypothesis. The then part contains
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 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 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 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 informationConjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence  a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
More 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 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 informationGeometry Review (1 st semester)
NAME HOUR Geometry Review (1 st semester) 1) The midpoint of XY is Z. If XY = n and XZ = n + 15, what is YZ? A) 18 B) 6 C) 45 D) 90 ) What is RS? A) 5 B) 56 C) D) 70 ) Which is an obtuse angle? A) PQR
More informationHigh 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
More information82 The Pythagorean Theorem and Its Converse. Find x.
Find x. 1. of the hypotenuse. The length of the hypotenuse is 13 and the lengths of the legs are 5 and x. 2. of the hypotenuse. The length of the hypotenuse is x and the lengths of the legs are 8 and 12.
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 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 informationDistance, Midpoint, and Pythagorean Theorem
Geometry, Quarter 1, Unit 1.1 Distance, Midpoint, and Pythagorean Theorem Overview Number of instructional days: 8 (1 day = 45 minutes) Content to be learned Find distance and midpoint. (2 days) Identify
More informationNCERT. not to be republished TRIANGLES UNIT 6. (A) Main Concepts and Results
UNIT 6 TRIANGLES (A) Main Concepts and Results The six elements of a triangle are its three angles and the three sides. The line segment joining a vertex of a triangle to the mid point of its opposite
More informationNCERT. not to be republished LINES AND ANGLES UNIT 5. (A) Main Concepts and Results
UNIT 5 LINES AND ANGLES (A) Main Concepts and Results An angle is formed when two lines or rays or line segments meet or intersect. When the sum of the measures of two angles is 90, the angles are called
More information51 Perpendicular and Angle Bisectors
51 Perpendicular and Angle Bisectors 51 Perpendicular and Angle Bisectors Warm Up Lesson Presentation Lesson Quiz Holt 51 Perpendicular and Angle Bisectors Warm Up Construct each of the following. 1.
More informationCCGPS UNIT 6 Semester 2 COORDINATE ALGEBRA Page 1 of 33. Connecting Algebra and Geometry Through Coordinates
GPS UNIT 6 Semester 2 OORDINTE LGER Page 1 of 33 onnecting lgebra and Geometry Through oordinates Name: Date: M912.G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example,
More informationClassify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.
ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. One angle of the triangle measures 90, so it is a right angle. Since the triangle has a
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 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 information1.1. Building Blocks of Geometry EXAMPLE. Solution a. P is the midpoint of both AB and CD. Q is the midpoint of GH. CONDENSED
CONDENSED LESSON 1.1 Building Blocks of Geometry In this lesson you will Learn about points, lines, and planes and how to represent them Learn definitions of collinear, coplanar, line segment, congruent
More information**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.
Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:
More informationAngles Formed by Intersecting Lines
COMMON CORE 1 3 Locker LESSON Common Core Math Standards The student is expected to: COMMON CORE GCO.C.9 Prove theorems about lines and angles. Mathematical Practices COMMON CORE 4.1 Angles Formed by
More informationCoordinate Coplanar Distance Formula Midpoint Formula
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the oneand twodimensional coordinate systems to
More informationFormal Geometry S1 (#2215)
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the Course Guides for the following course: Formal Geometry S1 (#2215)
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 information1.2 Inductive Reasoning
Page 1 of 6 1.2 Inductive Reasoning Goal Use inductive reasoning to make conjectures. Key Words conjecture inductive reasoning counterexample Scientists and mathematicians look for patterns and try to
More informationconditional statement conclusion Vocabulary Flash Cards Chapter 2 (p. 66) Chapter 2 (p. 69) Chapter 2 (p. 66) Chapter 2 (p. 76)
biconditional statement conclusion Chapter 2 (p. 69) conditional statement conjecture Chapter 2 (p. 76) contrapositive converse Chapter 2 (p. 67) Chapter 2 (p. 67) counterexample deductive reasoning Chapter
More informationUnit 6 Pythagoras. Sides of Squares
Sides of Squares Unit 6 Pythagoras Sides of Squares Overview: Objective: Participants discover the Pythagorean Theorem inductively by finding the areas of squares. TExES Mathematics Competencies II.004.A.
More information22 Proof Proof questions. This chapter will show you how to:
22 Ch22 537544.qxd 23/9/05 12:21 Page 537 4 4 3 9 22 537 2 2 a 2 b This chapter will show you how to: tell the difference between 'verify' and 'proof' prove results using simple, stepbystep chains of
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 informationA Correlation of Pearson Texas Geometry Digital, 2015
A Correlation of Pearson Texas Geometry Digital, 2015 To the Texas Essential Knowledge and Skills (TEKS) for Geometry, High School, and the Texas English Language Proficiency Standards (ELPS) Correlations
More 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 informationMiddle Grades Mathematics 5 9
Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from realworld situations. 2. Apply problemsolving strategies
More information(n = # of sides) One interior angle:
6.1 What is a Polygon? Regular Polygon Polygon Formulas: (n = # of sides) One interior angle: 180(n 2) n Sum of the interior angles of a polygon = 180 (n  2) Sum of the exterior angles of a polygon =
More information23 Conditional Statements. Identify the hypothesis and conclusion of each conditional statement. 1. If today is Friday, then tomorrow is Saturday.
Identify the hypothesis and conclusion of each conditional statement. 1. If today is Friday, then tomorrow is Saturday. 2. Hypothesis: Today is Friday. Conclusion: Tomorrow is Saturday. Hypothesis: 2x
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 informationLesson 13: Proofs in Geometry
211 Lesson 13: Proofs in Geometry Beginning with this lesson and continuing for the next few lessons, we will explore the role of proofs and counterexamples in geometry. To begin, recall the Pythagorean
More 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 informationGeometry and Spatial Reasoning
Mathematics TEKS Refinement 2006 68 Tarleton State University Geometry and Spatial Reasoning Activity: TEKS: Creating Venn Diagrams with Quadrilaterals (6.6) Geometry and spatial reasoning. The student
More informationvertex, 369 disjoint pairwise, 395 disjoint sets, 236 disjunction, 33, 36 distributive laws
Index absolute value, 135 141 additive identity, 254 additive inverse, 254 aleph, 466 algebra of sets, 245, 278 antisymmetric relation, 387 arcsine function, 349 arithmetic sequence, 208 arrow diagram,
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 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 informationSection 1. Statements and Truth Tables. Definition 1.1: A mathematical statement is a declarative sentence that is true or false, but not both.
M3210 Supplemental Notes: Basic Logic Concepts In this course we will examine statements about mathematical concepts and relationships between these concepts (definitions, theorems). We will also consider
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 informationNEW MEXICO Grade 6 MATHEMATICS STANDARDS
PROCESS STANDARDS To help New Mexico students achieve the Content Standards enumerated below, teachers are encouraged to base instruction on the following Process Standards: Problem Solving Build new mathematical
More informationHonors Geometry Final Exam Study Guide
20112012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.
More 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 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 informationChapter 1 Line and Angle Relationships
Chapter 1 Line and Angle Relationships SECTION 1.1: Sets, Statements, and Reasoning 1. a. Not a statement. b. Statement; true c. Statement; true d. Statement; false. a. Statement; true b. Not a statement.
More informationTest to see if ΔFEG is a right triangle.
1. Copy the figure shown, and draw the common tangents. If no common tangent exists, state no common tangent. Every tangent drawn to the small circle will intersect the larger circle in two points. Every
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 informationCumulative Test. 161 Holt Geometry. Name Date Class
Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 2 C 90 B 6 D 11 2. RM bisects VRQ. If mmrq 2, what is mvrm? F 41 H 9 G 2
More informationGeometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: Activity 24
Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: ctivity 24 esources: Springoard Geometry Unit Overview In this unit, students will study formal definitions of basic figures,
More information