What s Next? Example in class: 1, 1, 2, 3, 5, 8,,

Size: px
Start display at page:

Download "What s Next? Example in class: 1, 1, 2, 3, 5, 8,,"

Transcription

1 Name: Period: 2.1 Inductive Reasoning What s Next? Example in class: 1, 1, 2, 3, 5, 8,, What are the next two terms in each sequence? 1) 1, 10, 100, 1000,, 2) 7, 3, -1, -5, -9, -13,, 3) 1, 3, 6, 10, 15, 21,, 4) 32, 30, 26, 20, 12, 2,, 5) 1, 2, 4, 8, 16, 32,, 6) 1, 1, 1, 2, Use inductive reasoning to draw the next shape in each picture 7) 8) 9)

2 10) What is the next shape? 11) Which one of the numbers does not belong in the following series? Explain why. 3, 4, 8, 9, 10, 18, 19, 38 12) The price of eyeglass frames is based on a pattern. How much is the one labeled???? $221 $111 $212 $122??? 13) Remove 4 matchsticks so that you have 5 squares left. Once you find one solution, try to find another way to do the puzzle.

3 Name: Period: 2.2 Algebraic Proof Solve each equation. Write a justification for each step. The first one is done for you Example: 1) -5 = 3c + 1 1) Given 2) ) Subtraction Property of equality 3) -6 = 3c 3) Simplify 4) 3 3 4) Division Property of equality 5) -2 = c 5) Simplify 6) c = -2 6) Symmetric Property of Equality Take as many steps as you need to be complete and justify every step! 1) 2p 30 = -4p + 6 2) z 3 2 = 10

4 3) - (w + 3) = 72 4) ½ (b 16) = 13 5) Finish the proof to solve for n. Then find the length of RT. Write a justification for each step. Include as many steps as you need. 1) RS + ST = RT 1) Segment Addition Postulate 2) 5n + 30 = 9n 5 2) 3) 30 = 4n 5 3) 4) 4) Addition property of equality 5) = n 5) 6) n = 6) 7) RT = 7)

5 Name: Period: 2.3 Deductive Reasoning In problems 1 & 2, complete an algebraic proof to determine the solution of each equation. Please list each step you use, and justify each step with a reason. 1) 3(x + 2) 1 = 4(x + 6) ) 3 = m m 3) ABC is equilateral. Is ABD equilateral? Explain your answer with deductive reasoning.

6 4) I found this picture on the back of a package of goldfish crackers. Critique the reasoning. 5.) Find counter-examples to the following statements. a) All prime numbers are odd. b) All even numbers have a 2, 4, 6, or 8 in the ones digit place. c) All mammals have fur. d) If you are in Geometry at TVHS, then you are in Mrs. Dasse s classroom right now. 6.) Use the definition: A number is even if it is divisible by 2 to explain why 0 is an even number. 7.) To be eligible to hold the office of the president of the United States, a candidate must be 35 years old, be a natural born citizen, and must have been a U.S. resident for at least 14 years. Given this information what conclusions can you draw from the following scenario? Michael is not eligible to be the president of the United States even though Michael has lived in the United States for 16 years.

7 Name: Period: 2.4 Deductive Reasoning Four couples decided to go camping to the state forest one weekend. Each couple traveled in a different van and each chose a separate camping spot. The camping sites were all labeled with a space number and while they were in the same area, the sites were not touching. Using the clues and the grid below, determine the full name of each couple, the color of their van, and the number of their camping space. 1. Bill, who is not married to Laura, didn't drive a black van. 2. Chuck and his wife Brenda were not camped in space #35. Brenda's last name is not Forrest. 3. The Lewis couple, who drove a tan van, camped in space # Tom camped in a space numbered lower than the one Cindy camped in but higher than the couple who drove in the red van did. 5. Tom isn't married to Mary Tread. Steve Branch didn't drive a blue van. 6. The couple driving the black van camped in space #43.

8 Fill in the blank squares so that each row and each column contain all of the digits 1 thru 4 (or whatever the size of the puzzle is). The heavy lines indicate areas (called cages) that contain groups of numbers that can be combined (in any order) to produce the result shown in the cage, with the indicated math operation. For example, 8 means you can multiply the values together to produce 8. Numbers in cages may repeat, as long as they are not in the same row or column. Numbers in cages may repeat, as long as they are not in the same row or column.

9 Name: Period: 2.5 Geometric Proof Geometric Proof Take as many steps as you need to prove each statement. Provide a reason for each step 1. Given AB HY Prove AB = HY 2. Given m A = 30 and m B = m A Prove m B = 30. C... D A B 3. Given 1 and 2 form a linear pair Prove: 1 and 2 are supplementary 1) 1 and 2 form a linear pair 1) 2) AD and AB form a line 2) Definition of 3) m DAB = 3) Definition of 4) 4) Angle Addition Postulate 5) 5) Substitution (steps 3 & 4) 6) 1 and 2 are supplementary 6)

10 Given: JKL is a right angle, 2 3 Prove: 1 and 3 are complementary 1) JKL is a right angle 1) 2) m JKL = ) 3) 3) Angle Addition Postulate 4) m 1 + m 2 = ) 5) 2 3 5) 6) 6) Def. of s 7) m 1 + m 3 = ) 8) 8) Def. of 5. Given CD EF and CD FG Prove: F is the midpoint of EG 1) 1) 2) 2) 3) 3) Transitive 4) 4)

11 Name: Period: 2.6 Angle Pairs Angle Pair-adise 1) Supplementary Angles: Two angles whose measures sum to 180 o. Use the diagram above to prove that 2 angles which are each supplementary to a 3 rd angle must be congruent. 2) Vertical Angles: Two angles whose sides form two pairs of opposite rays Use the diagram at the right to prove that vertical angles are congruent. 3) Right angle: An angle whose measure is (aka Mr. S s Favorite theorem ) 1 Prove: All right angles are congruent. 2

12 4) Given: ABC is a right angle, find the measures of ABD and DBC 5) What type of angles are 1 and 2? Given: the m 1 = 2x + 3 and m 2 = 3x + 2 Find the m 3 6) What kind of angles are ABE and EBC? Given: m ABE = 2x + 5 and m EBC = x + 4 Find the m DBC 7) What kind of angles are DBC and ABD? Given: m ABD = 4x + 5 and m DBC = 2x + 1 Find m CBE 8) What kind of angles are 4 and 2? Given: m 4 = 5y 9 and m 2 = 2y + 3 Find m 3

13 Name: Period: 2.7 More Proofs Prove each statement: 1. Given that AB CD and CD, EF prove that AB EF Statements Reasons 2. Use the diagram to prove that LK JL Statements Reasons 3. Given that 3 = 40, 1 2, 2 3. Prove that m 1 = 40 Statements Reasons

14 4. Use the vertical angles theorem to prove that when 2 lines are perpendicular to one another, that all angles measure 90 Statements Reasons 5. Given that: UV XY, VW WX, WX YZ, prove UW XZ Complete the proof by correctly ordering the reasons to correspond with the correct statements. Statements 1. UV XY, VW WX, WX YZ 2. VW YZ 3. UV = XY, VW = YZ 4. UV + VW = XY + YZ 5. UV + VW = UW, XY + YZ = XZ 6. UW = XZ 7. UW XZ Reasons Reason choices Transitive property of congruence Addition (property of equality) Definition of congruent segments Given Segment addition postulate Definition of congruent segments Substitution property 6. Given the diagram at right, prove that AC = 2 BC. Statements Reasons

15 Geometry-reteaching angle relationships Name W e2c0[1m6i wknuztka\ hsmoufztpwoabrzew `LYLHCR.H T XAVlPlz _rxi`gbhatbsz trvecskerrnvleld]. 2.8 Angle Relationships Name the relationship: complementary, linear pair, vertical, or adjacent. 1) 2) a b a b 3) 4) b a b a Find the measure of angle b. 5) 6) b b 7) 8) 55 b 35 b ^ p2c0s1[6m dkqujtxah osjoqfztpwhadrze_ ylvlrcu.z N mafljli druivgqhmtjsn BrGeosieqr`vteZdx.\ R ]MdandUe^ ywwidtihf pitnyf^imneiqtje] ng`emoymleitmrxyx. -1- Worksheet by Kuta Software LLC

16 How are these angles related? Make an equation then find the value of x. 9) 10) (x + 17) 36 (5x + 1) (3x + 1) 11) 12) (3x + 2) 80 5x 38 13) 14) (x - 13) (x + 2) 15) 16) 2x 40 (4x + 2) 82 H f2u0u1f6d dkauntzal KS[omfVt]wVaKrSet ZLxLqCR.g N fahltla Fr[iNgghMtBsV [rsessxeyrqvoehdp.w P ^Mna[d[es uwmi\tdhr EIDnWfciknwi`tDeV RGPeUoVm]e\tzrWyv. -2- Worksheet by Kuta Software LLC

17 Name: Period: 2.9 Quiz Unit 2 Review 1.) Explain the difference between inductive and deductive reasoning. You may use an example to help explain the difference between the two. 2.) Find counter-examples to the following statements to prove them false. a) All angles are acute b) 3 x is a prime number for all values of x. c) All rational numbers have a decimal portion. 3.) Complete the patterns by drawing the next 2 steps. a) b) c) 4) Complete each sequence by writing in the next 2 terms a) -1, 4, -9, 16, -25,, b) 1, 2, 3, 4,, c) 1, 3, 6, 10,, d) 1, 5, 12, 22, 35,, 5) Complete the KenKen Puzzle

18 6) Prove that if 2 angles form a linear pair and are congruent, then they must be right angles. Hint: how many degrees go around a full rotation? 7) 8) 9) 10) 11) Complete the proof. (hint: how can you use the definition of supplementary?)

Notes: Review of Algebra I skills

Notes: Review of Algebra I skills Notes: Review of Algebra I skills http://www.monroeps.org/honors_geometry.aspx http://www.parklandsd.org/wp-content/uploads/hrs_geometry.pdf Name: Date: Period: Algebra Review: Systems of Equations * If

More information

Section 2-1. Chapter 2. Make Conjectures. Example 1. Reasoning and Proof. Inductive Reasoning and Conjecture

Section 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 information

1.4 Reasoning and Proof

1.4 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 information

2-6 Geometric Proof. Warm Up Lesson Presentation Lesson Quiz. Holt Geometry

2-6 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 information

2.4 Algebraic and Congruence Properties

2.4 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 information

Ready 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 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 information

Conditional statement:

Conditional statement: Conditional statement: Hypothesis: Example: If the sun is shining, then it must be daytime. Conclusion: Label the hypothesis and conclusion for each of the following conditional statements: 1. If a number

More information

HW Set #1: Problems #1-8 For #1-4, choose the best answer for each multiple choice question.

HW 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 information

Name: 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. 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 information

Unit 2: Geometric Reasoning Section 1: Inductive Reasoning

Unit 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 information

Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1

Geometry 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 information

Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES

Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Geometry Chapter 3 3-6: PROVE THEOREMS ABOUT PERPENDICULAR LINES Warm-Up 1.) What is the distance between the points (2, 3) and (5, 7). 2.) If < 1 and < 2 are complements, and m < 1 = 49, then what is

More information

Using Inductive and Deductive Reasoning

Using 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 information

(b) Follow-up visits: December, May, October, March. (c ) 10, 4, -2, -8,..

(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 information

right angle an angle whose measure is exactly 90ᴼ

right 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 information

Writing: 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? 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 information

ACTIVITY 15 Continued Lesson 15-2

ACTIVITY 15 Continued Lesson 15-2 Continued PLAN Pacing: 1 class period Chunking the Lesson Examples A, B Try These A B #1 2 Example C Lesson Practice TEACH Bell-Ringer Activity Read the introduction with students and remind them of the

More information

Mr. Northcutt's Math Classes Class Presentation

Mr. Northcutt's Math Classes Class Presentation Mr. Northcutt's Math Classes Class Presentation October 2, 2009 (22) Transition Math Math 1 Math 2 1 Transition Math Daily Summary Announcement(s): Retests: Can take a retest is you work with me or Ms.

More information

Geometry Midterm REVIEW

Geometry 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 information

GEOMETRY UNIT 1 WORKBOOK. CHAPTER 2 Reasoning and Proof

GEOMETRY 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 information

Geometry - Chapter 2 Earn-A-Try Test

Geometry - 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

Chapter 2. Reasoning and Proof

Chapter 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 information

2-5 Algebraic Proof. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry

2-5 Algebraic Proof. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry 2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Solve each equation. 1. 3x + 5 = 17 4. x = 4 2. r 3.5 = 8.7 r = 12.2 3. 4t 7 = 8t + 3 t = 5 2 n = 38 5. 2(y 5) 20 = 0 y = 15

More information

2-1 Using Inductive Reasoning to Make Conjectures

2-1 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 information

Chapter 2. Reasoning and Proof

Chapter 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 information

2-7 Flowchart and Paragraph Proofs

2-7 Flowchart and Paragraph Proofs 2-7 Flowchart and Paragraph Proofs Warm Up Lesson Presentation Lesson Quiz Geometry Angle Relationship Worksheet Math Warehouse Proof Quiz http://www.mathwarehouse.com/properties/p roperties-quiz.php Warm

More information

Proofs Practice Proofs Worksheet #2

Proofs Practice Proofs Worksheet #2 Name: No. Per: Date: Serafino Geometry M T W R F 2C Proofs Practice Proofs Worksheet #2 1. Given: O is the midpoint of MN Prove: OW = ON OM = OW 1. O is the midpoint of seg MN Given 2. Segment NO = Segment

More information

Geometry Study Guide. Name: Class: Date: Matching

Geometry 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 information

GEOMETRY CHAPTER 2 REVIEW / PRACTICE TEST

GEOMETRY 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 information

MTH 250 Graded Assignment 4

MTH 250 Graded Assignment 4 MTH 250 Graded Assignment 4 Measurement Material from Kay, sections 2.4, 3.2, 2.5, 2.6 Q1: Suppose that in a certain metric geometry* satisfying axioms D1 through D3 [Kay, p78], points A, B, C and D are

More information

Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31

Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31 Warm Up 1. deductive 2. D b. a and b intersect 1 and 2 are supplementary 2 and 3 are supplementary 3. I will go to the store; Law of Detachment Lesson Practice a. 1. 1 and 2 are. 2. 1 and 3 are. 3. m 1

More information

Chapter 2. Reasoning and Proof

Chapter 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 information

GEOMETRY CHAPTER 2: Deductive Reasoning

GEOMETRY 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 information

Find the next item in the pattern below. The red square moves in the counterclockwise direction. The next figure is.

Find 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 information

Algebraic Proof. Warm Up Solve each equation. Agenda: Warm-Up/Pull SG Algebraic Proofs Notes Practice Proofs. 1. 3x + 5 = 17.

Algebraic Proof. Warm Up Solve each equation. Agenda: Warm-Up/Pull SG Algebraic Proofs Notes Practice Proofs. 1. 3x + 5 = 17. Warm Up Solve each equation. 1. 3x + 5 = 17 4. x = 4 2. r 3.5 = 8.7 r = 12.2 3. 4t 7 = 8t + 3 t = 5 2 n = 38 Agenda: Warm-Up/Pull SG Algebraic Proofs Notes Practice Proofs 5. 2(y 5) 20 = 0 y = 15 Essential

More information

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date:

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date: NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST Name: Date: Day 1 1. Determine the value of x if ΔABC is equilateral. B 7.5x 6x + 3 A Write your answer on the line. 10x 5 C What is the

More information

Inductive 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 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 information

2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont.

2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont. 2.8 Proving angle relationships cont. ink.notebook page 84 page 83 2.8 cont. page 85 page 86 Lesson Objectives Standards Lesson Notes 2.8 Proving Angle Relationships Cont. Press the tabs to view details.

More information

Chapter 2 Segment Measurement and Coordinate Graphing

Chapter 2 Segment Measurement and Coordinate Graphing Geometry Concepts Chapter 2 Segment Measurement and Coordinate Graphing 2.2 Find length segments (1.3) 2.3 Compare lengths of segments (1.3) 2.3 Find midpoints of segments (1.7) 2.5 Calculate coordinates

More information

2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain.

2) 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 information

Day 1 Inductive Reasoning and Conjectures

Day 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 information

GH Chapter 2 Test Review-includes Constructions

GH 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 information

HONORS GEOMETRY CHAPTER 2 WORKBOOK

HONORS 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 information

Chapter 2 Practice Test

Chapter 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 information

Question 1 (3 points) Find the midpoint of the line segment connecting the pair of points (3, -10) and (3, 6).

Question 1 (3 points) Find the midpoint of the line segment connecting the pair of points (3, -10) and (3, 6). Geometry Semester Final Exam Practice Select the best answer Question (3 points) Find the midpoint of the line segment connecting the pair of points (3, -0) and (3, 6). A) (3, -) C) (3, -) B) (3, 4.5)

More information

Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?

Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y? Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel

More information

Chapter 6 Summary 6.1. Using the Hypotenuse-Leg (HL) Congruence Theorem. Example

Chapter 6 Summary 6.1. Using the Hypotenuse-Leg (HL) Congruence Theorem. Example Chapter Summary Key Terms corresponding parts of congruent triangles are congruent (CPCTC) (.2) vertex angle of an isosceles triangle (.3) inverse (.4) contrapositive (.4) direct proof (.4) indirect proof

More information

Geometry - Chapter 2 Corrective 1

Geometry - 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 information

Geometry. Unit 2- Reasoning and Proof. Name:

Geometry. 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 information

7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI.

7. 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 information

Parallel and Perpendicular Lines

Parallel 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 information

Chapter 2: Geometric Reasoning Review

Chapter 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 information

2.1 If Then Statements

2.1 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 information

Chapter Review #1-3. Choose the best answer.

Chapter 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 information

Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems

Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary

More information

Geometry CP Review WS

Geometry 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 information

Geometry Unit 2 Notes Logic, Reasoning and Proof

Geometry 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 information

p, p or its negation is true, and the other false

p, 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 information

2-1. Inductive Reasoning and Conjecture. Lesson 2-1. What You ll Learn. Active Vocabulary

2-1. 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 information

Review for Geometry Midterm 2015: Chapters 1-5

Review for Geometry Midterm 2015: Chapters 1-5 Name Period Review for Geometry Midterm 2015: Chapters 1-5 Short Answer 1. What is the length of AC? 2. Tell whether a triangle can have sides with lengths 1, 2, and 3. 3. Danny and Dana start hiking from

More information

Chapter 2. Worked-Out Solutions Quiz (p. 90)

Chapter 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 information

Segment Measurement, Midpoints, & Congruence

Segment Measurement, Midpoints, & Congruence Lesson 2 Lesson 2, page 1 Glencoe Geometry Chapter 1.4 & 1.5 Segment Measurement, Midpoints, & Congruence Last time, we looked at points, lines, and planes. Today we are going to further investigate lines,

More information

Geometry Unit 1 Segment 3 Practice Questions

Geometry 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 information

Chapter 1 Line and Angle Relationships

Chapter 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 5. Conditional 9. Simple 13. H: The

More information

2, 10, 30, 68, 130,...

2, 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 information

NAME DATE PERIOD. Inductive Reasoning and Conjecture. Make a conjecture based on the given information. Draw a figure to illustrate your conjecture.

NAME 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 information

Name: Class: Date: B. The twentieth term is A. D. There is not enough information.

Name: 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 information

8. C is the midpoint of BD. 4. AB < AE

8. C is the midpoint of BD. 4. AB < AE Assumptions and Justifications Use page 7 in your book to help complete the notes below Things You an Assume From a iagram Things You AN T Assume From a iagram I. For each picture list the facts you can

More information

Postulates, Definitions, and Theorems (Chapter 4)

Postulates, Definitions, and Theorems (Chapter 4) Postulates, Definitions, and Theorems (Chapter 4) Segment Addition Postulate (SAP) All segments AB and BC have unique real number measures AB and BC such that: ABCBC = AC if and only if B is between A

More information

Chapter 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. 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 information

Chapter 7. Geometric Inequalities

Chapter 7. Geometric Inequalities 4. Let m S, then 3 2 m R. Since the angles are supplementary: 3 2580 4568 542 Therefore, m S 42 and m R 38. Part IV 5. Statements Reasons. ABC is not scalene.. Assumption. 2. ABC has at least 2. Definition

More information

Examples: Identify three pairs of parallel segments in the diagram. 1. AB 2. BC 3. AC. Write an equation to model this theorem based on the figure.

Examples: Identify three pairs of parallel segments in the diagram. 1. AB 2. BC 3. AC. Write an equation to model this theorem based on the figure. 5.1: Midsegments of Triangles NOTE: Midsegments are also to the third side in the triangle. Example: Identify the 3 midsegments in the diagram. Examples: Identify three pairs of parallel segments in the

More information

Conditional Statement: Statements in if-then form are called.

Conditional 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 information

2.2 Day 1: Date: Geometry

2.2 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 information

Segment Measurement, Midpoints, & Congruence

Segment Measurement, Midpoints, & Congruence Lesson 2 Lesson 2, page 1 Glencoe Geometry Chapter 1.4 & 1.5 Segment Measurement, Midpoints, & Congruence Last time, we looked at points, lines, and planes. Today we are going to further investigate lines,

More information

Honors Geometry Semester Review Packet

Honors 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

Chapter 4 Reasoning and Proof Geometry

Chapter 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 information

Answers. Chapter 9 A92. Angles Theorem (Thm. 5.6) then XZY. Base Angles Theorem (Thm. 5.6) 5, 2. then WV WZ;

Answers. Chapter 9 A92. Angles Theorem (Thm. 5.6) then XZY. Base Angles Theorem (Thm. 5.6) 5, 2. then WV WZ; 9 9. M, 0. M ( 9, 4) 7. If WZ XZ, then ZWX ZXW ; Base Angles Theorem (Thm..6). M 9,. M ( 4, ) 74. If XZ XY, then XZY Y; Base Angles Theorem (Thm..6). M, 4. M ( 9, ) 7. If V WZV, then WV WZ; Converse of

More information

1-2 Measuring and Constructing Segments

1-2 Measuring and Constructing Segments 1-2 Measuring and Constructing Segments Warm Up Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint

More information

2015 Canadian Team Mathematics Contest

2015 Canadian Team Mathematics Contest The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 205 Canadian Team Mathematics Contest April 205 Solutions 205 University of Waterloo 205 CTMC Solutions Page 2 Individual Problems.

More information

The following statements are conditional: Underline each hypothesis and circle each conclusion.

The 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 information

Honors Geometry Mid-Term Exam Review

Honors 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 information

LESSON 2 5 CHAPTER 2 OBJECTIVES

LESSON 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 information

Chapter 6. Worked-Out Solutions AB 3.61 AC 5.10 BC = 5

Chapter 6. Worked-Out Solutions AB 3.61 AC 5.10 BC = 5 27. onstruct a line ( DF ) with midpoint P parallel to and twice the length of QR. onstruct a line ( EF ) with midpoint R parallel to and twice the length of QP. onstruct a line ( DE ) with midpoint Q

More information

Name: Geometry. Chapter 2 Reasoning and Proof

Name: 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 information

Chapters 1 & 2 Basics of Geometry & Reasoning/Proof

Chapters 1 & 2 Basics of Geometry & Reasoning/Proof 1 st Semester Chapters 1 & 2 Basics of Geometry & Reasoning/Proof Name: Teacher: Mrs. Gerardot or Mrs. Brown Period: Gerardot and Brown 1 1.2 Points Lines and Planes HW: 1.2 worksheet Point UNDEFINED Terms

More information

GEO 9 CH CH ASSIGNMENT SHEET GEOMETRY Points, Lines, Planes p all,15,16,17,21,25

GEO 9 CH CH ASSIGNMENT SHEET GEOMETRY Points, Lines, Planes p all,15,16,17,21,25 GEO 9 CH1-2.2 1 CH 1-2.2 ASSIGNMENT SHEET GEOMETRY 9 DAY SECTION NAME PAGE ASSIGNMENT 1 Algebra Review/Assignment #1 Handout 2 Algebra Review/Assignment #2 Handout 3 1.2 Points, Lines, Planes p. 7-8 1-10

More information

1. Find all solutions to 1 + x = x + 1 x and provide all algebra for full credit.

1. Find all solutions to 1 + x = x + 1 x and provide all algebra for full credit. . Find all solutions to + x = x + x and provide all algebra for full credit. Solution: Squaring both sides of the given equation gives + x = x 2 + 2x x + x which implies 2x x 2 = 2x x. This gives the possibility

More information

Geometry Unit 2 Notes Logic, Reasoning and Proof

Geometry 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 information

Homework 1 #3. v 10. Student Name/ID: Integrated Mathematics II / AIR Int Math II (Robertson) 1. Simplify.

Homework 1 #3. v 10. Student Name/ID: Integrated Mathematics II / AIR Int Math II (Robertson) 1. Simplify. Homework #3 Integrated Mathematics II / AIR Int Math II (Robertson) Student Name/ID:. Simplify. v 0 Assume that the variable represents a positive real number. H om ew or k #3 Page / 0 2. For each experiment,

More information

Homework 10: p.147: 17-41, 45

Homework 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 information

9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC.

9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC. 3. Sample answer: Solve 5x = 3x + 1; opposite sides of a parallelogram are congruent; es; You could start b setting the two parts of either diagonal equal to each other b the Parallelogram Diagonals Theorem

More information

Name Class Date. Additional Vocabulary Support. Reasoning in Algebra and Geometry

Name Class Date. Additional Vocabulary Support. Reasoning in Algebra and Geometry Additional Vocabulary Support Concept List Addition Property of Equality Division Property of Equality Reflexive Property of Equality Subtraction Property of Equality Transitive Property of Equality Distributive

More information

If two sides of a triangle are congruent, then it is an isosceles triangle.

If 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 information

Intro to Algebra Today. We will learn names for the properties of real numbers. Homework Next Week. Due Tuesday 45-47/ 15-20, 32-35, 40-41, *28,29,38

Intro to Algebra Today. We will learn names for the properties of real numbers. Homework Next Week. Due Tuesday 45-47/ 15-20, 32-35, 40-41, *28,29,38 Intro to Algebra Today We will learn names for the properties of real numbers. Homework Next Week Due Tuesday 45-47/ 15-20, 32-35, 40-41, *28,29,38 Due Thursday Pages 51-53/ 19-24, 29-36, *48-50, 60-65

More information

Unit 5: Congruency. Part 1 of 3: Intro to Congruency & Proof Pieces. Lessons 5-1 through 5-4

Unit 5: Congruency. Part 1 of 3: Intro to Congruency & Proof Pieces. Lessons 5-1 through 5-4 Name: Geometry Period Unit 5: Congruency Part 1 of 3: Intro to Congruency & Proof Pieces Lessons 5-1 through 5-4 In this unit you must bring the following materials with you to class every day: Please

More information

Unit 2 Definitions and Proofs

Unit 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 information

Lesson 9.1 Skills Practice

Lesson 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 information

Geometry Unit 2 Review Show all work and follow the criteria for credit.

Geometry Unit 2 Review Show all work and follow the criteria for credit. Competency 1: Angles and Angle Bisectors 1. What is the classification of an angle that has a measure of less than 90 o? 4. Given the diagram below where BD is an angle bisector. A D 2. Given the following

More information

Ch 2 Practice. Multiple Choice

Ch 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 information