Chapter 2-Reasoning and Proof
|
|
- Morgan Andrews
- 5 years ago
- Views:
Transcription
1 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 two lines intersect at right angles, then the two lines are perpendicular. a. Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right angles. b. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular. c. Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right angles. d. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not perpendicular. 2. Write this statement as a conditional in if-then form: All triangles have three sides. a. If a triangle has three sides, then all triangles have three sides. b. If a figure has three sides, then it is not a triangle. c. If a figure is a triangle, then all triangles have three sides. d. If a figure is a triangle, then it has three sides. 3. Which statement is a counterexample for the following conditional? If you live in Springfield, then you live in Illinois. a. Sara Lucas lives in Springfield. b. Jonah Lincoln lives in Springfield, Illinois. c. Billy Jones lives in Chicago, Illinois. d. Erin Naismith lives in Springfield, Massachusetts. 4. Draw a Draw a Venn diagram to illustrate this conditional: Cars are motor vehicles.
2 a. Motor vehicles Cars 5. Another name for an if-then statement is a. Every conditional has two parts. The part following if is the and the part following then is the. a. conditional; conclusion; hypothesis b. hypothesis; conclusion; conditional c. conditional; hypothesis; conclusion d. hypothesis; conditional; conclusion b. c. Motor vehicles Cars Cars 6. Which choice shows a true conditional with the hypothesis and conclusion identified correctly? a. Yesterday was Monday if tomorrow is Thursday. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Monday. b. If tomorrow is Thursday, then yesterday was Tuesday. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is not Thursday. c. If tomorrow is Thursday, then yesterday was Tuesday. Hypothesis: Yesterday was Tuesday. Conclusion: Tomorrow is Thursday. d. Yesterday was Tuesday if tomorrow is Thursday. Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday. Motor vehicles d. Motor Cars vehicles 7. What is the conclusion of the following conditional? A number is divisible by 3 if the sum of the digits of the number is divisible by 3. a. The number is odd. b. The sum of the digits of the number is divisible by 3. c. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. d. The number is divisible by 3.
3 8. What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. a. If a point is in the first quadrant, then its coordinates are positive. b. If a point is not in the first quadrant, then the coordinates of the point are not positive. c. If the coordinates of a point are positive, then the point is in the first quadrant. 9. What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then its measure is 90. a. If an angle is not a right angle, then its measure is 90. False b. If an angle is not a right angle, then its measure is not 90. True c. If an angle has measure 90, then it is a right angle. False d. If an angle has measure 90, then it is a right angle. True d. If the coordinates of a point are not positive, then the point is not in the first quadrant. 10. Which conditional has the same truth value as its converse? a. If x = 7, then. b. If a figure is a square, then it has four sides. c. If x 17 = 4, then x = 21. d. If an angle has measure 80, then it is acute. 11. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 3, then x 2 = 9. a. If x 2 = 9, then x = 3. True; x 2 = 9 if and only if x = 3. b. If x 2 = 3, then x = 9. False c. If x 2 = 9, then x = 3. True; x = 3 if and only if x 2 = 9. d. If x 2 = 9, then x = 3. False 12. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample. If two lines are parallel, they do not intersect. If two lines do not intersect, they are parallel. a. One statement is false. If two lines do not intersect, they could be skew.. b. One statement is false. If two lines are parallel, they may intersect twice. c. Both statements are true. Two lines are parallel if and only if they do not intersect. d. Both statements are true. Two lines are not parallel if and only if they do not intersect. 13. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample. If an angle is a right angle, its measure is 90. If an angle measure is 90, the angle is a right angle. a. One statement is false. If an angle measure is 90, the angle may be a vertical angle. b. One statement is false. If an angle is a right angle, its measure may be 180. c. Both statements are true. An angle is a right angle if and only if its measure is 90. d. Both statements are true. The measure of angle is 90 if and only if it is not a right angle. 14. Write the two conditional statements that make up the following biconditional. I drink juice if and only if it is breakfast time. a. I drink juice if and only if it is breakfast time. It is breakfast time if and only if I drink juice. b. If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice. c. If I drink juice, then it is breakfast time. I drink juice only if it is breakfast time. d. I drink juice. It is breakfast time. 15. When a conditional and its converse are true, you can combine them as a true. a. counterexample b. biconditional c. unconditional d. hypothesis 16. Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a true biconditional. Two lines that intersect at right angles are perpendicular. a. The statement is not reversible. b. Reversible; if two lines intersect at right angles, then they are perpendicular. c. Reversible; if two lines are perpendicular, then they intersect at right angles. d. Reversible; two lines intersect at right angles if and only if they are perpendicular.
4 17. Is the statement a good definition? If not, find a counterexample. A square is a figure with two pairs of parallel sides and four right angles. a. The statement is a good definition. b. No; a rhombus is a counterexample. c. No; a rectangle is a counterexample. d. No; a parallelogram is a counterexample. a. converse b. conditional c. biconditional d. counterexample 19. Which statement provides a counterexample to the following faulty definition? A square is a figure with four congruent sides. a. A six-sided figure can have four sides congruent. b. Some triangles have all sides congruent. c. A square has four congruent angles. d. A rectangle 18. One way to show that a statement is NOT a good has four sides. definition is to find a. 20. Which biconditional is NOT a good definition? a. A whole number is odd if and only if the number is not divisible by 2. b. An angle is straight if and only if its measure is 180. c. A whole number is even if and only if it is divisible by 2. d. A ray is a bisector of an angle if and only if it splits the angle into two angles. Fill in each missing reason. 21. Given:,, and. Find x. P R Q S Drawing not to scale x 5 + x 11 = 100 2x 16 = 100 2x = 116 x = 58 a. b. Substitution Property c. Simplify d. e. Division Property of Equality a. Angle Addition Postulate; Subtraction Property of Equality b. Protractor Postulate; Addition Property of Equality c. Angle Addition Postulate; Addition Property of Equality d. Protractor Postulate; Subtraction Property of Equality 22. Given: Prove: a. a. Given
5 b. Symmetric Property of Equality c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality b. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Symmetric Property of Equality c. a. Given b. Substitution Property c. Subtraction Property of Equality d. Division Property of Equality e. Reflexive Property of Equality d. a. Given b. Substitution Property c. Subtraction Property of Equality d. Addition Property of Equality e. Symmetric Property of Equality 23. Name the Property of Equality that justifies the statement: If p = q, then. a. Reflexive Property b. Multiplication Property c. Symmetric Property d. Subtraction Property 24. Which statement is an example of the Addition Property of Equality? a. If p = q then b. If p = q then. c. If p = q then d. p = q 25. Name the Property of Congruence that justifies the statement: If. a. Symmetric Property b. Transitive Property c. Reflexive Property d. none of these 26. Name the Property of Congruence that justifies the statement: If. a. Transitive Property b. Symmetric Property c. Reflexive Property d. none of these Use the given property to complete the statement. 27. Transitive Property of Congruence If. a. b. c. d. 28. Multiplication Property of Equality If, then. a. b. c. d. 29. Substitution Property of Equality If, then. a. b. c. d. (7x 8) (6x + 11) Drawing not to scale a. 19 b. 125 c. 19 d Find 30. bisects = 7x. =. Find a. 50 b. 125 c. 75 d Find the value of x. Drawing not to scale
6 a. 37 b. 143 c. 27 d Find the values of x and y. a. x = 15, y = 17 b. x = 112, y = 68 c. x = 68, y = 112 d. x = 17, y = 15 4y 7x Short Answer Drawing not to scale 34. Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample. If x = 4, then x 2 = Write the converse of the given true conditional and decide whether the converse is true or false. If the converse is true, combine it with the conditional to form a true biconditional. If the converse is false, give a counterexample. If the probability that an event will occur is 0, then the event is impossible to occur. Fill in each missing reason. 36. Given: 2x 6x + 8 (2x) Drawing not to scale 6(x 3) Drawing not to scale 38. Complete the paragraph proof. Given: Prove: are supplementary, and are supplementary. 37. Given:
7 40. Write the conditional statement that the Venn diagram illustrates. Quadrilaterals By the definition of supplementary angles, (a) and (b). Then by (c). Subtract from each side. You get (d), or (e). Squares 39. Solve for x. Justify each step. Essay 41. Given: are complementary, and are complementary. Prove: Fill in each missing reason. 42. Given: Prove:
8 Drawing not to scale Other 43. a. Write the following conditional in if-then form. b. Write its converse in if-then form. c. Determine the truth value of the original conditional and its converse. Explain why each of them is true or false, and provide a counterexample(s) for any false statement(s). On a number line, the points with coordinates 2 and 5 are 7 units apart. 44. Write the two conditional statements that form the given biconditional. Then decide whether the biconditional is a good definition. Explain. Three points are collinear if and only if they are coplanar.
9 Chapter 2-Reasoning and Proof Answer Section MULTIPLE CHOICE 1. ANS: B REF: 2-1 Conditional Statements OBJ: Conditional Statements 2. ANS: D REF: 2-1 Conditional Statements OBJ: Conditional Statements 3. ANS: D REF: 2-1 Conditional Statements OBJ: Conditional Statements 4. ANS: A REF: 2-1 Conditional Statements OBJ: Conditional Statements 5. ANS: C REF: 2-1 Conditional Statements OBJ: Conditional Statements 6. ANS: D REF: 2-1 Conditional Statements OBJ: Conditional Statements 7. ANS: D REF: 2-1 Conditional Statements OBJ: Conditional Statements 8. ANS: C REF: 2-1 Conditional Statements OBJ: Converses 9. ANS: D REF: 2-1 Conditional Statements OBJ: Converses 10. ANS: C REF: 2-1 Conditional Statements OBJ: Converses 11. ANS: D REF: 2-2 Biconditionals and Definitions OBJ: Writing Biconditionals 12. ANS: A REF: 2-2 Biconditionals and Definitions OBJ: Writing Biconditionals 13. ANS: C REF: 2-2 Biconditionals and Definitions OBJ: Writing Biconditionals 14. ANS: B REF: 2-2 Biconditionals and Definitions OBJ: Writing Biconditionals 15. ANS: B REF: 2-2 Biconditionals and Definitions OBJ: Writing Biconditionals 16. ANS: D REF: 2-2 Biconditionals and Definitions OBJ: Recognizing Good Definitions 17. ANS: C REF: 2-2 Biconditionals and Definitions OBJ: Recognizing Good Definitions 18. ANS: D REF: 2-2 Biconditionals and Definitions OBJ: Recognizing Good Definitions 19. ANS: A REF: 2-2 Biconditionals and Definitions OBJ: Recognizing Good Definitions 20. ANS: D REF: 2-2 Biconditionals and Definitions OBJ: Recognizing Good Definitions 21. ANS: C REF: 2-4 Reasoning in Algebra 22. ANS: B REF: 2-4 Reasoning in Algebra 23. ANS: D REF: 2-4 Reasoning in Algebra 24. ANS: B REF: 2-4 Reasoning in Algebra 25. ANS: A REF: 2-4 Reasoning in Algebra 26. ANS: A REF: 2-4 Reasoning in Algebra 27. ANS: C REF: 2-4 Reasoning in Algebra 28. ANS: C REF: 2-4 Reasoning in Algebra 29. ANS: C REF: 2-4 Reasoning in Algebra 30. ANS: D REF: 2-4 Reasoning in Algebra 31. ANS: C REF: 2-5 Proving Angles Congruent OBJ: Theorems About Angles STA: CA GEOM 1.0 CA GEOM 2.0 CA GEOM 4.0
10 32. ANS: A REF: 2-5 Proving Angles Congruent OBJ: Theorems About Angles STA: CA GEOM 1.0 CA GEOM 2.0 CA GEOM ANS: A REF: 2-5 Proving Angles Congruent OBJ: Theorems About Angles STA: CA GEOM 1.0 CA GEOM 2.0 CA GEOM 4.0 SHORT ANSWER 34. ANS: If x 2 = 16, then x = 4. False; if x 2 = 16, then x can be equal to 4. REF: 2-1 Conditional Statements OBJ: Converses 35. ANS: If an event is impossible, the probability of the event is 0. True An event is impossible if and only if the probability of the event is zero. REF: 2-2 Biconditionals and Definitions 36. ANS: a. Angle Addition Postulate b. Substitution Property c. Distributive Property d. Simplify e. Addition Property of Equality f. Division Property of Equality REF: 2-4 Reasoning in Algebra STA: CA GEOM 1.0 CA GEOM ANS: a. Segment Addition Postulate b. Substitution c. Simplify d. Subtraction Property of Equality e. Division Property of Equality OBJ: Writing Biconditionals OBJ: Connecting Reasoning in Algebra and Geometry REF: 2-4 Reasoning in Algebra OBJ: Connecting Reasoning in Algebra and Geometry STA: CA GEOM 1.0 CA GEOM ANS: a. 180 b. 180 c. Transitive Property (or Substitution Property) d. e. REF: 2-5 Proving Angles Congruent OBJ: Theorems About Angles STA: CA GEOM 1.0 CA GEOM 2.0 CA GEOM ANS: Given Addition Property of Equality Simplify
11 x = 27 Division Property of Equality Simplify REF: 2-4 Reasoning in Algebra OBJ: Connecting Reasoning in Algebra and Geometry STA: CA GEOM 1.0 CA GEOM ANS: If a figure is a square, then it is a quadrilateral. REF: 2-1 Conditional Statements OBJ: Conditional Statements ESSAY 41. ANS: [4] By the definition of complementary angles, and. By the Transitive Property of Equality (or Substitution Property),. By the Subtraction Property of Equality,, and by the definition of congruent angles. OR equivalent explanation [3] one step missing OR one incorrect justification [2] two steps missing OR two incorrect justifications [1] correct steps with no explanations REF: 2-5 Proving Angles Congruent OBJ: Theorems About Angles STA: CA GEOM 1.0 CA GEOM 2.0 CA GEOM ANS: [4] a. Given b. Substitution Property c. Vertical Angles Theorem d. Substitution Property [3] three parts correct [2] two parts correct [1] one part correct REF: 2-5 Proving Angles Congruent OBJ: Theorems About Angles STA: CA GEOM 1.0 CA GEOM 2.0 CA GEOM 4.0 OTHER 43. ANS: a. On a number line, if points have coordinates 2 and 5, then they are 7 units apart. b. On a number line, if points are 7 units apart, then they have coordinates 2 and 5. c. The original conditional is true by the Ruler Postulate. The converse is false. The points 0 and 7 and 7 units apart, but their coordinates are not 2 and 5. REF: 2-1 Conditional Statements OBJ: Converses 44. ANS: If three points are collinear, then they are coplanar.
12 If three points are coplanar, then they are collinear. The biconditional is not a good definition. Three coplanar points might not lie on the same line. REF: 2-2 Biconditionals and Definitions OBJ: Recognizing Good Definitions
Foundations 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 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 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 informationChapter 2 Test Review
Chapter 2 Test Review 1. If then what are and The diagram is not to scale. A., C., B., D., 2. How are the two angles related? 60 120 Drawing not to scale A. supplementary C. vertical B. adjacent D. complementary
More informationChapter 2 Test Review 1. Based on the pattern, what are the next two terms of the sequence? 8, 15, 22, 29,...
Number of Customers Geometry Honors Name: Chapter 2 Test Review 1. Based on the pattern, what are the next two terms of the sequence? 8, 15, 22, 29,... 2. Based on the pattern, what is the next figure
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 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 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 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 informationWarm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
2-4 Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Write a conditional statement from each of the following. 1. The intersection of two lines is a point. If two lines intersect, then they intersect
More informationGeometry First Semester Exam Review
Geometry First Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name three points that are collinear. a. points T, Q, and R c. points
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 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 information2-4. Holt McDougal Geometry
Warm Up Write a conditional statement from each of the following. 1. The intersection of two lines is a point. If two lines intersect, then they intersect in a point. 2. An odd number is one more than
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 information7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI.
1. Name three points in the diagram that are not collinear. 2. If RS = 44 and QS = 68, find QR. 3. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition
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 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 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 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 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 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 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 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 informationCN#4 Biconditional Statements and Definitions
CN#4 s and Definitions OBJECTIVES: STUDENTS WILL BE ABLE TO WRITE AND ANALYZE BICONDITIONAL STATEMENTS. Vocabulary biconditional statement definition polygon triangle quadrilateral When you combine a conditional
More informationGeometry Note Cards EXAMPLE:
Geometry Note Cards EXAMPLE: Lined Side Word and Explanation Blank Side Picture with Statements Sections 12-4 through 12-5 1) Theorem 12-3 (p. 790) 2) Theorem 12-14 (p. 790) 3) Theorem 12-15 (p. 793) 4)
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 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 - 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 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 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 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 informationTest Review: Geometry L2 Period 1 and 3 Test Date: Friday November 6
Test Review: Geometry L2 Period 1 and 3 Test Date: Friday November 6 Things it would be a good idea to know: 1) All terms, definitions, properties, postulates, theorems from Unit 1 and Unit 2 2) How to
More informationGeometry Lesson 1.4A Thurday, August 20, 2015
Geometry: Module 1 Lesson 4 Bellwork: Angle measures and angle bisectors Explain 1: 1) Discuss some random (but necessary) theorems and postulates 2) Understand Conditional Statements 3) Understand difference
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 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 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 information1.5 Related Conditionals
Name Class Date 1.5 Related Conditionals Essential Question: How are conditional statements related to each other? Explore G.4.B Identify and determine the validity of the converse, inverse, and contrapositive
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 informationGeometry Cumulative Study Guide Test 8
Geometry Cumulative Study Guide Test 8 Numeric Response 1. A rectangular plot of land has a length of 3.5 miles and a width of 8.5 miles. What is the area, in square miles, of the plot of land? 2. A circle
More informationChapter 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 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 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 informationGeometry Cumulative Review
Geometry Cumulative Review Name 1. Find a pattern for the sequence. Use the pattern to show the next term. 1, 3, 9, 27,... A. 81 B. 45 C. 41 D. 36 2. If EG = 42, find the value of y. A. 5 B. C. 6 D. 7
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 informationGeometry Unit 1 Practice
Lesson 1-1 1. Persevere in solving problems. Identify each figure. hen give all possible names for the figure. a. S Geometry Unit 1 Practice e. P S G Q. What is a correct name for this plane? W R Z X b..
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 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 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 informationNational Benchmark Test 1. 1 Which three-dimensional figure does this net produce? Name: Date: Copyright by Pearson Education Page 1 of 13
National enchmark Test 1 Name: ate: 1 Which three-dimensional figure does this net produce? opyright 2005-2006 by Pearson Education Page 1 of 13 National enchmark Test 1 2 Which of the following is a net
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 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 informationHonors Geometry Mid-Term Exam Review
Class: Date: Honors Geometry Mid-Term Exam Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Classify the triangle by its sides. The
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 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 informationName: Class: Date: 5. If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28. a. True b.
Indicate whether the statement is true or false. 1. If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square. 2. If M and N are midpoints of sides and of, then. 3. The
More information1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3. a cm b cm c cm d. 21.
FALL SEMESTER EXAM REVIEW (Chapters 1-6) CHAPTER 1 1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3 2. Find the length of PQ. a. 50.9 cm b. 46.3 cm c. 25.7 cm
More informationGeometry Midterm REVIEW
Name: Class: Date: ID: A Geometry Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given LM = MP and L, M, and P are not collinear. Draw
More informationGeometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1
Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1 Multiple Choice. Identify the choice that best completes the statement or answers the question. 1. Which statement(s)
More informationLesson 9.1 Skills Practice
Lesson 9.1 Skills Practice Name Date Earth Measure Introduction to Geometry and Geometric Constructions Vocabulary Write the term that best completes the statement. 1. means to have the same size, shape,
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 informationName: Date: Period: 1. In the diagram below,. [G.CO.6] 2. The diagram below shows a pair of congruent triangles, with and. [G.CO.
Name: Date: Period: Directions: Read each question carefully and choose the best answer for each question. You must show LL of your work to receive credit. 1. In the diagram below,. [G.CO.6] Which statement
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 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 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 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 informationB C. You try: What is the definition of an angle bisector?
US Geometry 1 What is the definition of a midpoint? The midpoint of a line segment is the point that divides the segment into two congruent segments. That is, M is the midpoint of if M is on and M M. 1
More informationGeometry 21 - More Midterm Practice
Class: Date: Geometry 21 - More Midterm Practice 1. What are the names of three planes that contain point A? 6. If T is the midpoint of SU, what are ST, TU, and SU? A. ST = 7, TU = 63, and SU = 126 B.
More informationSUBAREA I MATHEMATIC REASONING AND COMMUNICATION Understand reasoning processes, including inductive and deductive logic and symbolic logic.
SUBAREA I MATHEMATIC REASONING AND COMMUNICATION 0001. Understand reasoning processes, including inductive and deductive logic and symbolic logic. Conditional statements are frequently written in "if-then"
More information2.2 Definitions and Biconditional Statements. Geometry Mr. Peebles 03/20/13
2.2 Definitions and Biconditional Statements Geometry Mr. Peebles 03/20/13 Geometry Bell Ringer Write the Contrapositive of the following conditional statement: If the polygon has three sides, then it
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 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 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 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 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 GENERAL GEOMETRY
Geometry GENERAL GEOMETRY Essential Vocabulary: point, line, plane, segment, segment bisector, midpoint, congruence I can use the distance formula to determine the area and perimeters of triangles and
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 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 informationGeometry CP - Ch. 4 Review
Geometry CP - Ch. 4 Review 1. If, which of the following can you NOT conclude as being true? A. B. C. D. 2. A. B. C. D. 3. Given and, find the length of QS and TV. A. 7 B. 25 C. 8 D. 2 4. The two triangles
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 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 information1. Grab board/marker for your group 2. Do WarmUp below
1. Grab board/marker for your group 2. Do WarmUp below TP bisects VS and MR. VM is congruent to SR. MP = 9, VT = 6 Perimeter of MRSV = 62 V T S Find VM. M P R Paragraph Proof D (2x) x 60 A B C Given: Diagram
More informationName: GEOMETRY: EXAM (A) A B C D E F G H D E. 1. How many non collinear points determine a plane?
GMTRY: XM () Name: 1. How many non collinear points determine a plane? ) none ) one ) two ) three 2. How many edges does a heagonal prism have? ) 6 ) 12 ) 18 ) 2. Name the intersection of planes Q and
More informationInductive Reasoning. Courage is resistance to fear, mastery of fear, not absence of fear. Mark Twain
Inductive Reasoning Courage is resistance to fear, mastery of fear, not absence of fear. Mark Twain Inductive Reasoning O Inductive Reasoning is the process of observing a pattern and making a conjecture
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 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 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 informationGeometry 1st semester Exam review game questions
Class: Date: Geometry 1st semester Exam review game questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name the Property of Equality that justifies
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 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 2 Find the length of each segment in the quadrilateral using the Distance Formula or the Ruler Postulate. JK = 3 1 = 4 KL = 3 4 = 7
Geometry 1st Edition Martin Gay SOLUTIONS MANUAL Full download at: https://testbankreal.com/download/geometry-1st-edition-martin-gaysolutions-manual/ Section 2.1 Practice 1. a. Use the perimeter formula
More informationName: Date: Period: ID: REVIEW CH 1 TEST REVIEW. 1. Sketch and label an example of each statement. b. A B. a. HG. d. M is the midpoint of PQ. c.
Name: Date: Period: ID: REVIEW CH 1 TEST REVIEW 1 Sketch and label an example of each statement a HG b A B c ST UV d M is the midpoint of PQ e Angles 1 and 2 are vertical angles f Angle C is a right angle
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 informationGeometry Voic Mr. R. and Mr. K
2.1 Using Inductive Reasoning to Make Conjectures Learning Goal: Use inductive reasoning to identify patterns, make conjectures and find counterexamples to disprove conjectures. Video: http://player.discoveryeducation.com/index.cfm?guidassetid=b1b5f95d-f72e-4d18-b220-ff73204e9a74
More informationName: 2015 Midterm Review Period: Date:
GEOMETRY Name: 2015 Midterm Review Period: Date: To be prepared for your midterm, you will need to PRACTICE PROBLEMS and STUDY TERMS from the following chapters. Use this guide to help you practice. UNIT
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 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 informationray part of a line that begins at one endpoint and extends infinitely far in only one direction.
1.1 Getting Started A 1 F m point location in space. E line The {set} of infinite points arranged in a straight figure that extends infinitely far in both directions. which each point is assigned a numerical
More informationSeptember 27, =2. x={ -2,2}
2. 1 1=2 x={ -2,2} What is a conditional statement? An if - then statement Conditional Statement If 0you are not completely satisfied with your math education, then you can have your money back. - ^ hypothesis
More information