Inductive Reasoning. Courage is resistance to fear, mastery of fear, not absence of fear. Mark Twain
|
|
- Darrell Barker
- 5 years ago
- Views:
Transcription
1 Inductive Reasoning Courage is resistance to fear, mastery of fear, not absence of fear. Mark Twain
2 Inductive Reasoning O Inductive Reasoning is the process of observing a pattern and making a conjecture about the pattern. O A conjecture is an unproven statement based on observations. O So, inductive reasoning is the process of observing a pattern and making an unproven statement about the pattern.
3 O Ex. 1: Describe the pattern and either draw the next shape or write the next three numbers. 1) 5, 15, 45, 135,.. 1) 405, 1215, ) -2, 1, 4, 7, 3) 10, 13, 16 4)
4 O Ex. 2: Make and test conjectures for each problem below. 1) The sum of two odd numbers. 3+5=8 7+9=16-5+7=2 The sum of two odd numbers is even. 1) The product of two even numbers. 4x6=24 8x8=64-4x4=-16 The product of two even numbers is even. 1) The sum of three consecutive odd numbers =3(5) 1+3+5=3(3) =3(17) The sum of three consecutive odd numbers is three times the middle number.
5 Counter-example O A counter-example is the case that shows a conjecture to be false. O Conjecture: The product of any two numbers is always positive. O Counter-example: -5 x 4 = -20 O Conjecture: We have school each weekday. O Counter-example: October 10th
6 O Ex. 3: Find the counter example to each conjecture. 1) All prime numbers are odd. 1) 2 2) If the sum of two numbers is even, then both of those numbers are also even. 1) 3+5=8 1) The sum of three consecutive numbers is always odd. 1) 3+4+5=12
7 Summary O You should now be able to: O Identify patterns and make conjectures about those patterns. O Provide counter-examples to false conjectures.
8 Conditional Statements The great use of life is to spend it for something that will outlast it. William James
9 Conditional statements O Each conditional statement has a condition and a consequence. O Hypothesis: is the condition of the statement (also the if portion of the if-then format). O Conclusion: is the consequence of the statement (also the then portion of the if-then format) O Example: All mammals have hair. O If-then form: If an animal is a mammal, then it has hair.
10 Ex. 1: For each conditional statement, write it in if-then form. 1) Every student at Westfield has to take Physical Science their freshman year. 1) If a student is a freshman at Westfield, then they have to take Physical Science. 2) Two angles are complementary if their measures add up to 90. 1) If two angle measures sum to be 90, then they are complementary angles 3) Vertical angles have two pairs of opposite rays. 1) If a pair of angles are vertical angles, then they have two pairs of opposite rays. 4) 2x+5=2, because x=-6 1) If x=-6, then 2x+5=2
11 Negation O A negation is the opposite of the original statement. O The apple is red. O Negation: the apple is NOT red.
12 Converse, Inverse, and Contrapositive. O Conditional statement: If I forget to put my name on a paper, then I get a zero for that paper. O Converse: switch the hypothesis and conclusion of the original conditional statement. O If I get a zero for a paper, then I forget to put my name on the paper. O Inverse: Negate BOTH the hypothesis and the conclusion of the original conditional statement. O If I remember to put my name on a paper, then I will not get a zero for that paper. O Contrapositive: Negate BOTH the hypothesis and the conclusion of the converse. O If I get greater than a zero on a paper, then I remember to put my name on the paper.
13 Ex. 2: For each conditional statement, write its converse, inverse, and contrapositive and decide each statements truth value. 1) If you watch this video, then you take notes for geometry. 1) Converse: If you take notes for geometry, then you watch this video. 2) Inverse: If you don t watch this video, then you don t take notes for geometry. 3) Contrapositive: If you don t take notes for geometry, then you don t watch this video.
14 Equivalent and Biconditional O Equivalent statements are statements that are both true or are both false. The conditional statement and contrapositive are always equivalent. The inverse and converse are always equivalent. O Biconditional statements are statements that the original conditional statement and its converse are both true. O For example: If two angle measures sum to be 90, then they are complementary. O The definition could be written as: Two angles are complementary if and only if (iff) their measures sum to 90.
15 Ex. 3: For each conditional statement, write its converse, inverse, and contrapositive and decide each statements truth value. If both the conditional and its converse are true, write a biconditional statement. 1) If four points are coplanar, then they lie in the same plane. 1) Converse: If four points lie in the same plane, then they are coplanar. 2) Inverse: If four points aren t coplanar, then they don t lie in the same plane,. 3) Contrapositive: If four points don t lie in the same plane, then they aren t coplanar. 4) Biconditional: Four points are coplanar iff they lie in the same plane.
16 Summary O At this point, you should be able to: O Write a converse, inverse, and contrapositive to a conditional statement. O Know the requirements for a statement to be biconditional. O Know how to negate a statement.
17 Deductive Reasoning Only the person who has faith in himself is able to be faithful to others. Erich Fromm
18 Deductive Reasoning O Deductive reasoning uses facts, definitions, properties, and laws of logic to form a logical argument.
19 Laws of Logic O Law of detachment: If the hypothesis of a true conditional statement is true, then the conclusion is also true. O If the flipped method proves to improve learning, then Mr. H will continue it for the whole year. O If Mr. H gets a haircut, then pigs can fly.
20 Law of Syllogism (dominoes) For want of a nail the shoe was lost. For want of a shoe the horse was lost. For want of a horse the rider was lost. For want of a rider the message was lost. For want of a message the battle was lost. For want of a battle the kingdom was lost. O These statements could be combined to be: For want of a nail, the kingdom was lost.
21 Law of Syllogism (dominoes) O If q, then r. O If r, then s. O If q, then s.
22 Ex. 1: Use the Law of Detachment to make a valid conclusion. 1) If two angles have the same measure, then they are congruent. The measure of angle A is 90 and the measure of angle B is 90. 1) Angle A is congruent to angle B. 2) Pythagoras takes a nap at 4pm. It is 4pm on Saturday. 1) Pythagoras is taking a nap.
23 Ex. 2: Use the Law of Syllogism to make a valid conclusion. 1) If two angles are both right angles, then they have the same measure. If two angles have the same measure, then they are congruent. 1) If two angles are both right angles, then they are congruent. 2) If Jesse get a job, then he can afford a car. If Jesse can afford a car, then he buys a car. 1) If Jesse gets a job, then he buys a car.
24 Ex. 3: Determine whether each statement is the result of inductive or deductive reasoning. Explain why. 1) For the last two weeks Mr. H has gone around helping students during the class period. You conclude that Mr. H will help students during the class period on Monday. 1) Inductive because you are making a conjecture based on previous observations. 2) The rule at work is that you have to work the full week to get paid on Friday. You were paid on Friday. Therefore, you went to all of your classes. 1) Deductive because you use rules and facts to make a conclusion.
25 Summary O You should be able to use the laws of logic to make valid conclusions. O You should be able to determine the difference between deductive and inductive reasoning.
26 Using Postulates and Diagrams A hero is no braver than an ordinary man (or woman), but he (/she) is brave five minutes longer. Ralph Waldo Emerson
27 Postulates 5-11 O 5: Through any two points there exists exactly one line. O 6: A line contains at least two points. O 7: If two lines intersect, then their intersection is exactly one point. O 8: Through any three noncollinear points there exists exactly one plane.
28 Postulates 5-11 O 9: A plane contains at least three noncollinear points. O 10: If two points lie in a plane, then the line containing them lies in the plane. O 11: If two planes intersect, then their intersection is a line.
29 O Ex. 1: State the postulate illustrated by the diagram. 1) A B 2) A B A C C B
30 O Ex. 2: Use the diagram to write examples of postulate 5 and 7. Through points C and B there is one line called line l. Line DE and Line BF intersect at point D.
31 O Ex. 3: Use the diagram to determine if each statement is true or false. 1) Line AB lies in plane R 2) Line FH lies in plane R 3) Line AC and Line FG will intersect. 4) Line GH is perpendicular to plane R. 5) Angle LGH is a right angle. 6) Angle LGH and angle LGF are supplementary angles. L
32 Summary O You should be able to identify the postulate used in drawing a diagram.
33 Reasoning using Algebra. Certain signs precede certain events. Cicero
34 Algebraic Properties of Equality. Let a, b, and c be real numbers. 1) Addition Property 2) Subtraction Property 3) Multiplication Property 4) Division Property 5) Substitution Property 6) Distributive Property 1) If a = b, then a + c = b + c. 2) If a = b, then a c = b c. 3) If a = b, then ac = bc. 4) If a = b and c 0, then a c = b c. 5) If a=b, then a can be sustitud ed in for any equation or expression. 6) a b + c = ab + ac
35 Example 1: Solve 2x + 30 = 75 3x. Write a reason for each step. Equation 2x + 30 = 75 3x 5x + 30 = 75 5x = 45 x = 9 Reason Given Addition Property Subtraction Property Division Property
36 Example 2: Solve 2(x + 30) = 2(70 3x). Write a reason for each step. Equation 2(x + 30) = 2(70 3x) 2x 60 = 140 6x 4x 60 = 140 4x = 200 x = 50 Reason Given Distributive Property Addition Property Addition Property Division Property
37 Reflexive Properties of Equality. 1) Real Numbers 2) Segment Length 3) Angle Measure 1) For any real number a, a = a. 2) For any segment AB, AB = AB 3) For any angle A, m A = m A.
38 Symmetric Properties of Equality. 1) Real Numbers 2) Segment Length 3) Angle Measure 1) For any real number a and b, a = b, then b = a. 2) For any segment AB and CD, if AB = CD, then CD = AB. 3) For any angle A and B, if m A = m B, then m B = m A.
39 Transitive Properties of Equality. 1) Real Numbers 2) Segment Length 3) Angle Measure 1) If a = b and b = c, then a = c. 2) IfAB = CD and CD = EF, then AB = EF. 3) If m A = m B and m B = m C, then m A = m C.
40 Example 3: Determine if m ABC= m FBD. Show your reasoning. A 1 F 2 C B 3 Equation m 1= m 3 m ABC= m 1+ m 2 m FBD= m 2 +m 3 m FBD= m 2+ m 1 m ABC= m FBD D Reason Given Angle Addition Postulate Angle Addition Postulate Substitution Property Transitive Property
41 Summary O You should be able to use properties to justify your reasoning. O You should be able to solve a problem and provide reasons for each step.
42 Prove Statements about segments and angles Anxiety is fear of one s self. Wilhelm Stekel
43 Congruence of Segments and Angles. (Theorem 2.1 and 2.2) 1) Reflexive Property of Congruence 2) Symmetric Property of Congruence 3) Transitive Property of Congruence For any segment AB and any angle A. 1) AB AB or A A 2) If AB CD, then CD AB or If A B, then B A 3) If AB CD and CD EF, then AB EF or If A B and B C, then A C.
44 Example 1: Use a two column proof to show that AC BD. A B C D Statements 1) AB = CD 2) AC = AB + BC 3) BD = CD + BC 4) BD = AB + BC 5) AC = BD 6) AC BD Reasons 1) Given 2) Segment Addition Postulate 3) Segment Addition Postulate 4) Substitution Property 5) Transitive Property 6) Definition of Congruence
45 Ex. 2: Name the property illustrated by the statement. 1) If F G and G H, then F H. 2) If EF GH, then GH EF. 3) AB AB
46 Example 1:Prove that AB=2AM. You know that M is the midpoint of AB. A M B Statements 1) M is a midpoint of AB. 2) AM MB 3) AM = MB 4) AB = AM + MB 5) AB = AM + AM 6) AB = 2AM Reasons 1) Given 2) Definition of Midpoint 3) Definition of congruence 4) Segment Addition Postulate 5) Substitution Property 6) Simplify
47 Summary O You should be able to prove statements about segments and angles. O You should be able to write a two column proof.
48 Prove Angle Pair Relationships. Remember that happiness is a way of travel not a destination. Roy M. Goodman
49 Theorem O Theorem 2.3: Right Angles Congruence Theorem. O All right angles are congruent. O Theorem 2.4: Congruent Supplements Theorem. O If two angles are supplementary to the same angle (or to congruent angles), then they are congruent. O Theorem 2.5: Congruent Complements Theorem. O If two angles are complementary to the same angle (or to congruent angles), then they are congruent.
50 1) Ex. 1: Prove that 1 3, given that 1 and 2 are supplementary and 3 and 2 are supplementary Statements 1) 1 and 2 are supp. 3 and 2 are supp. 2) m 1 + m 2 = 180 3) m 3 + m 2 = 180 4) m 1 + m 2 = m 3 + m 2 5) m 1 = m 3 6) 1 3 1) Given Reasons 2) Definition of Supplementary 3) Definition of Supplementary 4) Transitive Property 5) Subtraction Property 6) Definition of Congruence
51 Postulate 12 and Theorem 2.6 O Postulate 12: Linear Pair Postulate. O If two angles form a linear pair, then they are supplementary. O Theorem 2.6: Vertical Angles Congruence Theorem. O Vertical Angles are Congruent.
52 O Ex. 2: Given that angle 3 and angle 4 are a linear pair and measure of angle 4 is 112, find the measure of angle 3. Statements 1) 3 and 4 form a linear pair and m 4 = 112 2) 3 and 4 are supp. 3) m 3 + m 4 = 180 4) m = 180 5) m 3 = 68 1) Given Reasons 2) Linear Pair Postulate 3) Definition of Supplementary 4) Substitution Property 5) Subtraction Property
53 Ex. 3: Find the value of x if m 1 = (3x 4) and m 4 = (6x 184). Statements 1) m 1 = 3x 4 2) m 4 = (6x 184) 3) 1 4 4) m 1 = m 4 5) 3x 4 = (6x 184) 6) 4 = 3x 184 7) 180=3x 8) 60=x Reasons 1) Given 2) Given 3) Vertical Angle Congruence Theorem 4) Definition of Congruence 5) Transitive Property 6) Subtraction Property 7) Addition Property 8) Division Property
54 Summary O You should be able to identify complementary and supplementary angles. O You should be able to identify linear pairs and vertical angles. O You should be able to use the above definitions, postulates, and theorems to write a proof.
Chapter 2: Reasoning and Proof
Name: Chapter 2: Reasoning and Proof Guided Notes Geometry Fall Semester 2.1 Use Inductive Reasoning CH. 2 Guided Notes, page 2 Term Definition Example conjecture An unproven statement that is based on
More informationGeometry: Notes
Geometry: 2.1-2.3 Notes NAME 2.1 Be able to write all types of conditional statements. Date: Define Vocabulary: conditional statement if-then form hypothesis conclusion negation converse inverse contrapositive
More information2-1 Using Inductive Reasoning to Make Conjectures
CHAPTER 2 Chapter Review 2-1 Using Inductive Reasoning to Make Conjectures Find the next term in each pattern. 1. 6, 12, 18,... 2. January, April, July,... 3. The table shows the score on a reaction time
More informationGeometry Unit 1 Segment 3 Practice Questions
Name: Class: _ Date: _ Geometry Unit 1 Segment 3 Practice Questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Based on the pattern, what are the
More informationGeometry - Chapter 2 Earn-A-Try Test
Name: Geometry - Chapter 2 Earn-A-Try Test Multiple Choice Identify the choice that best completes the statement or answers the question. Use CAPITAL letters only!! Ex: A,B,C,D; Not a,b,c,d. 1. Write a
More information(b) Follow-up visits: December, May, October, March. (c ) 10, 4, -2, -8,..
Geometry Honors - Chapter 2 Reasoning and Proof Section 2-1 Inductive Reasoning and Conjecture I can explore inductive and deductive reasoning. I can find counterexamples to disprove conjectures. I can
More informationGeometry Unit 2 Notes Logic, Reasoning and Proof
Geometry Unit 2 Notes Logic, Reasoning and Proof Review Vocab.: Complementary, Supplementary and Vertical angles. Syllabus Objective: 2.1 - The student will differentiate among definitions, postulates,
More informationGeometry Unit 2 Notes Logic, Reasoning and Proof
Geometry Unit Notes Logic, Reasoning and Proof Review Vocab.: Complementary, Supplementary and Vertical angles. Syllabus Objective:. - The student will justify conjectures and solve problem using inductive
More informationGeometry. Unit 2- Reasoning and Proof. Name:
Geometry Unit 2- Reasoning and Proof Name: 1 Geometry Chapter 2 Reasoning and Proof ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (2-1)
More informationFind the next item in the pattern below. The red square moves in the counterclockwise direction. The next figure is.
CHAPTER 2 Study Guide: Review Organizer Objective: Help students organize and review key concepts and skills presented in Chapter 2. Online Edition Multilingual Glossary Countdown Week 4 Vocabulary biconditional
More informationChapter 2. Reasoning and Proof
Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9
More informationGeometry Study Guide. Name: Class: Date: Matching
Name: Class: Date: ID: A Geometry Study Guide Matching Match each vocabulary term with its definition. a. conjecture e. biconditional statement b. inductive reasoning f. hypothesis c. deductive reasoning
More informationChapter 2. Reasoning and Proof
Chapter 2 Reasoning and Proof 2.1 Inductive Reasoning 2.2 Analyze Conditional Statements 2.3 Apply Deductive Reasoning 2.4 Use Postulates and Diagrams 2.5 Algebraic Proofs 2.6 Segments and Angles Proofs
More informationDay 1 Inductive Reasoning and Conjectures
Formal Geometry Chapter 2 Logic and Proofs Day 1 Inductive Reasoning and Conjectures Objectives: SWBAT form a conjecture, and check it SWBAT use counterexamples to disprove a conjecture Logic the use of
More informationChapter 2. Reasoning and Proof
Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9
More informationName: Class: Date: B. The twentieth term is A. D. There is not enough information.
Class: Date: Chapter 2 Review 1. Based on the pattern, what are the next two terms of the sequence? 9, 15, 21, 27,... A. 33, 972 B. 39, 45 C. 162, 972 D. 33, 39 2. What conjecture can you make about the
More informationUsing Inductive and Deductive Reasoning
Big Idea 1 CHAPTER SUMMARY BIG IDEAS Using Inductive and Deductive Reasoning For Your Notebook When you make a conjecture based on a pattern, you use inductive reasoning. You use deductive reasoning to
More informationThe following statements are conditional: Underline each hypothesis and circle each conclusion.
Geometry Unit 2 Reasoning and Proof 2-1 Conditional Statements Conditional Statement a statement which has a hypothesis and conclusion, often called an if-then statement. Conditional statements are contain
More informationSection 2-1. Chapter 2. Make Conjectures. Example 1. Reasoning and Proof. Inductive Reasoning and Conjecture
Chapter 2 Reasoning and Proof Section 2-1 Inductive Reasoning and Conjecture Make Conjectures Inductive reasoning - reasoning that uses a number of specific examples to arrive at a conclusion Conjecture
More informationGeometry - Chapter 2 Corrective 1
Name: Class: Date: Geometry - Chapter 2 Corrective 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Make a table of values for the rule x 2 16x + 64 when
More informationp, p or its negation is true, and the other false
Logic and Proof In logic (and mathematics) one often has to prove the truthness of a statement made. A proposition is a (declarative) sentence that is either true or false. Example: An odd number is prime.
More informationNAME DATE PERIOD. Inductive Reasoning and Conjecture. Make a conjecture based on the given information. Draw a figure to illustrate your conjecture.
2-1 NAME DATE PERIOD Skills Practice Inductive Reasoning and Conjecture Make a conjecture about the next item in each sequence. 1. 2. 4, 1, 2, 5, 8 3. 6, 1 1, 5, 9 2 2,4 4. 2, 4, 8, 16, 32 Make a conjecture
More informationUnit 2: Geometric Reasoning Section 1: Inductive Reasoning
Unit 2: Geometric Reasoning Section 1: Inductive Reasoning Ex #1: Find the next item in the pattern. January, March, May,... Ex #2: Find the next item in the pattern. 7, 14, 21, 28, Ex #3: Find the next
More informationGeometry CP Review WS
Geometry CP 2.1-2.5 Review WS Name 1. a) Use inductive reasoning to sketch the fourth figure in each pattern. Figure 4 b) How many squares are in the next object? 2. Use inductive reasoning to write the
More informationChapter 2: Geometric Reasoning Review
Geometry B Name: Date: Block: Chapter 2: Geometric Reasoning Review Show all work to receive full credit. This will be collected. 1) What is the next item in the pattern? 1, 2, 4, 8,... 2) Find the next
More informationFormal Geometry. Conditional Statements
Formal Geometry Conditional Statements Objectives Can you analyze statements in if then form? Can you write the converse, inverse, and contrapositive of if then statements? Inductive Reasoning Inductive
More informationGeometry Unit 2 Notes Logic, Reasoning and Proof
Geometry Unit Notes Logic, Reasoning and Proof Review Vocab.: Complementary, Supplementary and Vertical angles. Syllabus Objective:. - The student will justify conjectures and solve problem using inductive
More informationright angle an angle whose measure is exactly 90ᴼ
right angle an angle whose measure is exactly 90ᴼ m B = 90ᴼ B two angles that share a common ray A D C B Vertical Angles A D C B E two angles that are opposite of each other and share a common vertex two
More informationChapter 2. Worked-Out Solutions Quiz (p. 90)
2.1 2.3 Quiz (p. 90) 1. If-then form: If an angle measures 167, then the angle is an obtuse angle. (True) Converse: If an angle is obtuse, then the angle measures 167. (False) Inverse: If an angle does
More informationChapter 2 Practice Test
Name: Class: Date: ID: A Chapter 2 Practice Test 1. What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 4 is also divisible by 8. 2. What is the conclusion of the following
More informationHONORS GEOMETRY CHAPTER 2 WORKBOOK
HONORS GEOMETRY CHAPTER 2 WORKBOOK FALL 2016 Chapter 2 Miscellaneous: The Structure of Geometry Vocabulary Definition Example Elements: 1. Deductive Structure Postulate (axiom) Example: Definitions Reversed:
More informationGeometry Test Unit 2 Logic, Reasoning and Proof
Geometry Test Unit 2 Logic, Reasoning and Proof Name: Date: Pd: Definitions (1-4) 1) Conditional Statement 2) Inductive Reasoning 3) Contrapositive 4) Logically equivalent statements 5) State the hypothesis
More informationName: Geometry. Chapter 2 Reasoning and Proof
Name: Geometry Chapter 2 Reasoning and Proof ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (2-1) Inductive Reasoning and Conjecture Pg
More informationConditional Statement: Statements in if-then form are called.
Monday 9/21 2.2 and 2.4 Wednesday 9/23 2.5 and 2.6 Conditional and Algebraic Proofs Algebraic Properties and Geometric Proofs Unit 2 Angles and Proofs Packet pages 1-3 Textbook Pg 85 (14, 17, 20, 25, 27,
More information2.2 Day 1: Date: Geometry
2.2 Day 1: Date: Geometry A Conditional Statement is an statement. The is the part following if. The is the part following then. Ex 1). What are the hypothesis and the conclusion of the conditional statement?
More informationChapter 2. Chapter 2 Section 2, pages Chapter 2 Section 3, pages
Geometry Unit 2 Targets & Info Name: This Unit s theme Reasoning and Proof September 9 September 30 (Approximate Time for Test) Use this sheet as a guide throughout the chapter to see if you are getting
More information2.1 If Then Statements
Chapter Deductive Reasoning Learn deductive logic Do your first - column proof New Theorems and Postulates **PUT YOUR LAWYER HAT ON!!. If Then Statements Recognize the hypothesis and conclusion of an ifthen
More informationGEOMETRY CHAPTER 2 REVIEW / PRACTICE TEST
GEOMETRY CHAPTER 2 REVIEW / PRACTICE TEST Name: Date: Hour: SECTION 1: Rewrite the conditional statement in If-Then Form. Then write its Converse, Inverse, and Contrapositive. 1) Adjacent angles share
More informationChapter 2 Review. Short Answer Determine whether the biconditional statement about the diagram is true or false.
Chapter 2 Review Short Answer Determine whether the biconditional statement about the diagram is true or false. 1. are supplementary if and only if they form a linear pair. 2. are congruent if and only
More informationHomework 10: p.147: 17-41, 45
2-4B: Writing Proofs Homework 10: p.147: 17-41, 45 Learning Objectives: Analyze figures to identify and use postulates about points, lines and planes Analyze and construct viable arguments in several proof
More informationReasoning and Proof Unit
Reasoning and Proof Unit 1 2 2 Conditional Statements Conditional Statement if, then statement the if part is hypothesis the then part is conclusion Conditional Statement How? if, then Example If an angle
More informationChapter 2 Study Guide and Review
State whether each sentence is true or false If false, replace the underlined term to make a true sentence 1 The first part of an if-then statement is the conjecture The first part of an if-then statement
More informationLOGIC. 11 Converse, Inverse, Contrapositve. 12/13 Quiz Biconditional Statements
Name Period GP LOGIC I can define, identify and illustrate the following terms Conditional Statement Hypothesis Conclusion Inductive Reasoning Deductive Reasoning Inverse Converse Contrapositive Biconditional
More informationIf two sides of a triangle are congruent, then it is an isosceles triangle.
1. What is the hypothesis of the conditional statement If two sides of a triangle are congruent, then it is an isosceles triangle. two sides of a triangle are congruent it is an isosceles triangle If two
More informationReady to Go On? Skills Intervention 2-1 Using Inductive Reasoning to Make Conjectures
Ready to Go On? Skills Intervention 2-1 Using Inductive Reasoning to Make Conjectures Find these vocabulary words in Lesson 2-1 and the Multilingual Glossary. Vocabulary inductive reasoning conjecture
More information2-1. Inductive Reasoning and Conjecture. Lesson 2-1. What You ll Learn. Active Vocabulary
2-1 Inductive Reasoning and Conjecture What You ll Learn Scan Lesson 2-1. List two headings you would use to make an outline of this lesson. 1. Active Vocabulary 2. New Vocabulary Fill in each blank with
More informationCh 2 Practice. Multiple Choice
Ch 2 Practice Multiple Choice 1. For the conditional statement, write the converse and a biconditional statement. If a figure is a right triangle with sides a, b, and c, then a 2 + b 2 = c 2. a. Converse:
More informationCMA Geometry Unit 1 Introduction Week 2 Notes
CMA Geometry Unit 1 Introduction Week 2 Notes Assignment: 9. Defined Terms: Definitions betweenness of points collinear points coplanar points space bisector of a segment length of a segment line segment
More informationGEOMETRY. 2.1 Conditional Statements
GEOMETRY 2.1 Conditional Statements ESSENTIAL QUESTION When is a conditional statement true or false? WHAT YOU WILL LEARN owrite conditional statements. ouse definitions written as conditional statements.
More information2-6 Geometric Proof. Warm Up Lesson Presentation Lesson Quiz. Holt Geometry
2-6 Geometric Proof Warm Up Lesson Presentation Lesson Quiz Warm Up Determine whether each statement is true or false. If false, give a counterexample. 1. It two angles are complementary, then they are
More informationG E O M E T R Y CHAPTER 2 REASONING AND PROOF. Notes & Study Guide CHAPTER 2 NOTES
G E O M E T R Y CHAPTER 2 REASONING AND PROOF Notes & Study Guide 2 TABLE OF CONTENTS CONDITIONAL STATEMENTS... 3 DEFINTIONS & BICONDITIONAL STATEMENTS... 6 DEDUCTIVE REASONING... 9 REASONING WITH PROPERTIES
More informationLESSON 2 5 CHAPTER 2 OBJECTIVES
LESSON 2 5 CHAPTER 2 OBJECTIVES POSTULATE a statement that describes a fundamental relationship between the basic terms of geometry. THEOREM a statement that can be proved true. PROOF a logical argument
More informationInductive Reasoning. Inductive Reasoning. Inductive Reasoning. Inductive Reasoning. Logic (with Truth Tables) If-Then Statements
Intro to Proofs (t-charts and paragraph) www.njctl.org Table of Contents When asked a question you don't know the answer to: 1) You can take a known to be true. Using conjecture is Contents Bob is taller
More information2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain.
1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 3) Explain why a four-legged
More informationGEOMETRY UNIT 1 WORKBOOK. CHAPTER 2 Reasoning and Proof
GEOMETRY UNIT 1 WORKBOOK CHAPTER 2 Reasoning and Proof 1 2 Notes 5 : Using postulates and diagrams, make valid conclusions about points, lines, and planes. I) Reminder: Rules that are accepted without
More information2, 10, 30, 68, 130,...
Geometry Unit 4: Reasoning Unit 4 Review Mathematician: Period: Target 1: Discover patterns in a sequence of numbers and figures Directions: Determine what type of is displayed in the given tables. 1)
More informationStudy Guide and Review
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. 1. A postulate is a statement that requires proof. A postulate is a statement that does not
More informationNAME DATE PER. 1. ; 1 and ; 6 and ; 10 and 11
SECOND SIX WEEKS REVIEW PG. 1 NME DTE PER SECOND SIX WEEKS REVIEW Using the figure below, identify the special angle pair. Then write C for congruent, S for supplementary, or N for neither. d 1. ; 1 and
More informationChapter 5 Vocabulary:
Geometry Week 11 ch. 5 review sec. 6.3 ch. 5 review Chapter 5 Vocabulary: biconditional conclusion conditional conjunction connective contrapositive converse deductive reasoning disjunction existential
More information1.4 Reasoning and Proof
Name Class Date 1.4 Reasoning and Proof Essential Question: How do you go about proving a statement? Explore Exploring Inductive and Deductive Reasoning Resource Locker A conjecture is a statement that
More informationUnit 2: Logic and Reasoning. start of unit
Unit 2: Logic and Reasoning Prior Unit: Introduction to Geometry Next Unit: Transversals By the end of this unit I will be able to: Skill Self-Rating start of unit Date(s) covered Self-Rating end of unit
More informationUnit 1: Introduction to Proof
Unit 1: Introduction to Proof Prove geometric theorems both formally and informally using a variety of methods. G.CO.9 Prove and apply theorems about lines and angles. Theorems include but are not restricted
More informationParagraph Proof, Two-Column Proof, Construction Proof, and Flow Chart Proof
.3 Forms of Proof Paragraph Proof, Two-Column Proof, Construction Proof, and Flow Chart Proof Learning Goals Key Terms In this lesson, you will: Use the addition and subtraction properties of equality.
More informationGeometry/Trigonometry Unit 2: Parallel Lines Notes Period:
Geometry/Trigonometry Unit 2: Parallel Lines Notes Name: Date: Period: # (1) Pg 108 109 #1-10 all (2) Pg 108 109 #12-22 Even and 30, 32 (3) Pg 114 #1-6; 9-13 (4) Pg 114-115 #15-18; 20; 22; 24; 26; 29 and
More informationChapter 2-Reasoning and Proof
Chapter 2-Reasoning and Proof Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the hypothesis and conclusion of this conditional statement: If
More informationFoundations of Math 3 -- Proof Practice
Foundations of Math 3 -- Proof Practice Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the hypothesis and conclusion of this conditional statement:
More informationthe plant on day 10 of the experiment
Lesson 2-1 Patterns Find the next two terms in each sequence. 1. 12, 17, 22, 27, 32,... 2. 1, 1.1, 1.11, 1.111, 1.1111,... 3. 5000, 1000, 200, 40,... 4. 1, 12, 123, 1234,... 5. 3, 0.3, 0.03, 0.003,...
More informationChapter 4 Reasoning and Proof Geometry
Chapter 4 Reasoning and Proof Geometry Name For 1 & 2, determine how many dots there would be in the 4 th and the 10 th pattern of each figure below. 1. 2. 3. Use the pattern below to answer the following:
More informationĚ /DZ RI 6\OORJLVP p. 60. Ě 5HIOH[LYH 3URSHUW\ p. 65 Ě conclusion, p. 49. Ě QHJDWLRQ p. 49. Ě 6\PPHWULF 3URSHUW\ p. 65 Ě conditional, p.
Topic 2 Review TOPIC VOCBULRY Ě biconditional, p. 55 Ě GHGXFWLYH UHDVRQLQJ p. 60 Ě /DZ RI 6\OORJLVP p. 60 Ě 5HIOH[LYH 3URSHUW\ p. 65 Ě conclusion, p. 49 Ě GLDPHWHU p. 44 Ě QHJDWLRQ p. 49 Ě 6\PPHWULF 3URSHUW\
More informationParallel and Perpendicular Lines
Cumulative Test Choose the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew. D A
More informationPre-AP Geometry Chapter 2 Test Review Important Vocabulary: Conditional Converse Hypothesis Conclusion Segment Addition
1 Pre-AP Geometry Chapter 2 Test Review Important Vocabulary: Conditional Converse Hypothesis Conclusion Segment Addition Midpoint Postulate Right Angle Opposite Rays Angle Bisector Angle Addition Complementary
More informationChapter Review #1-3. Choose the best answer.
Chapter Review #1- Choose the best answer. 1. Which statement is NOT true? A Parallel lines do not intersect. B A segment has exactly two endpoints. C Two planes that do not intersect are always skew.
More information2.4 Algebraic and Congruence Properties
2.4 Algebraic and Congruence Properties Learning Objectives Understand basic properties of equality and congruence. Solve equations and justify each step in the solution. Use a 2-column format to prove
More informationGEOMETRY CHAPTER 2: Deductive Reasoning
GEOMETRY CHAPTER 2: Deductive Reasoning NAME Page 1 of 34 Section 2-1: If-Then Statements; Converses Conditional Statement: If hypothesis, then conclusion. hypothesis conclusion converse conditional statement
More informationGeometry Chapter 2 2-3: APPLY DEDUCTIVE REASONING
Geometry Chapter 2 2-3: APPLY DEDUCTIVE REASONING Warm-up Any Definition can be written as a Biconditional Statement. For Warm-up: Write some of our past vocabulary terms as Biconditional statements. Terms:
More informationStudy Guide and Review
State whether each sentence is or false. If false, replace the underlined term to make a sentence. 1. A postulate is a statement that requires proof. A postulate is a statement that does not require a
More informationHW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question.
Geometry Homework Worksheets: Chapter 2 HW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question. 1. Which of the following statements is/are always true? I. adjacent
More informationWriting: Answer each question with complete sentences. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line?
Writing: Answer each question with complete sentences. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary
More informationChapter 2 Review - Formal Geometry
*This packet is due on the day of the test:. It is worth 10 points. ALL WORK MUST BE SHOWN FOR FULL CREDIT!!! Multiple Choice Identify the choice that best completes the statement or answers the question.
More information2.1 Practice A. Name Date. In Exercises 1 and 2, copy the conditional statement. Underline the hypothesis and circle the conclusion.
Name ate.1 Practice In Exercises 1 and, copy the conditional statement. Underline the hypothesis and circle the conclusion. 1. If you like the ocean, then you are a good swimmer.. If it is raining outside,
More informationProvide (write or draw) a counterexample to show that the statement is false.
Geometry SOL G.1 G.3a Study Guide Name: Date: Block: SHOW ALL WORK. Use another piece of paper as needed. SECTION 1: G.1 1. Provide (write or draw) a counterexample to show that the statement is false.
More informationChapter Test. Chapter Tests LM 5 4, }} MO 5 14, } LN Answers. In Exercises 4 6, use the diagram. Geometry Benchmark Tests
Chapter Test For use after Chapter. Which of the following is not an undefined term? A. Point B. Plane C. Line D. Ray. Which of the following is an undefined term? A. Line B. Ray C. Segment D. Intersection
More informationUnit 2 Definitions and Proofs
2.1-2.4 Vocabulary Unit 2 efinitions and Proofs Inductive reasoning- reasoning based on examples, experience, or patterns to show that that a rule or statement is true Conjecture a statement you believe
More informationGeometry Chapters 1 & 2 Test
Class: Date: Geometry Chapters 1 & 2 Test 1. How many cubes would you use to make the structure below? A. 15 cubes B. 16 cubes C. 17 cubes D. 18 cubes 2. What are the names of three planes that contain
More information2. If a rectangle has four sides the same length, then it is a square. 3. If you do not study, then you do not earn good grades.
Name: Period: Geometry Unit 2: Reasoning and Proof Homework Section 2.1: Conditional and Biconditional Statements Write the converse of each conditional. 1. If you eat spinach, then you are strong. 2.
More informationGH Chapter 2 Test Review-includes Constructions
Name: Class: Date: Show All Work. Test will include 2 proofs from the proof practice worksheet assigned week of 9/8. GH Chapter 2 Test Review-includes Constructions ID: A 1. What is the value of x? State
More information2 2 Practice Conditional Statements Form G Answers
2 2 PRACTICE CONDITIONAL STATEMENTS FORM G ANSWERS PDF - Are you looking for 2 2 practice conditional statements form g answers Books? Now, you will be happy that at this time 2 2 practice conditional
More informationGraphic Organizer: Reasoning and Proof Unit Essential Quetions
Start Here Page 1 Graphic Organizer: Reasoning and Proof Unit Essential Quetions Right Side of Page Right Sight Page 2 Unit 2 Reasoning and Proof (handout: orange sheet) Right side Right Sight Page 3 Proof
More informationGeometry Chapter 2 Practice Free Response Test
Geometry Chapter 2 Practice Free Response Test Directions: Read each question carefully. Show ALL work. No work, No credit. This is a closed note and book test.. Identify Hypothesis and Conclusion of the
More information2.1 Practice B. 1. If you like to eat, then you are a good cook. 2. If an animal is a bear, then it is a mammal.
hapter.1 Start Thinking Sample answer: If an animal is a horse, then it is a mammal; If an animal is not a mammal, then it cannot be a horse. Any fact stated in the form of an "if-then" statement could
More informationGEOMETRY. 2.5 Proving Statements about Segments and Angles
GEOMETRY 2.5 Proving Statements about Segments and Angles ESSENTIAL QUESTION How can I prove a geometric statement? REVIEW! Today we are starting proofs. This means we will be using ALL of the theorems
More informationConditional Statements
2.1 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G.4.B Conditional Statements Essential Question When is a conditional statement true or false? A conditional statement, symbolized by p q, can be written as an
More informationAnswer each of the following problems. Make sure to show your work. 2. What does it mean if there is no counterexample for a conjecture?
Answer each of the following problems. Make sure to show your work. 1. What is a conjecture? 2. What does it mean if there is no counterexample for a conjecture? 3. What purpose would be served by a counterexample
More informationMidpoint M of points (x1, y1) and (x2, y2) = 1 2
Geometry Semester 1 Exam Study Guide Name Date Block Preparing for the Semester Exam Use notes, homework, checkpoints, quizzes, and tests to prepare. If you lost any of the notes, reprint them from my
More information3. Understand The Laws of Detachment and Syllogism 4. Appreciate a simple Ham Sandwich.
Lesson 4 Lesson 4, page 1 of 8 Glencoe Geometry Chapter 2.2 and 2.3 If-Then Statements & Deductive Reasoning By the end of this lesson, you should be able to 1. Write a statement in if-then Form. 2. To
More informationCumulative Test. 101 Holt Geometry. Name Date Class
Choose the best answer. 1. Which of PQ and QR contains P? A PQ only B QR only C Both D Neither. K is between J and L. JK 3x, and KL x 1. If JL 16, what is JK? F 7 H 9 G 8 J 13 3. SU bisects RST. If mrst
More information1. Based on the pattern, what are the next two terms of the sequence?,... A. C. B. D.
Semester Exam I / Review Integrated Math II 1. Based on the pattern, what are the next two terms of the sequence?,... B. D. 2. Alfred is practicing typing. The first time he tested himself, he could type
More informationDISCOVERING GEOMETRY Over 6000 years ago, geometry consisted primarily of practical rules for measuring land and for
Name Period GEOMETRY Chapter One BASICS OF GEOMETRY Geometry, like much of mathematics and science, developed when people began recognizing and describing patterns. In this course, you will study many
More informationHonors Geometry Semester Review Packet
Honors Geometry Semester Review Packet 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear
More information- involve reasoning to a contradiction. 1. Emerson is the tallest. On the assumption that the second statement is the true one, we get: 2. 3.
Math 61 Section 3.1 Indirect Proof A series of lessons in a subject that contradicted each other would make that subject very confusing. Yet, in reasoning deductively in geometry, it is sometimes helpful
More information