GEOMETRY CHAPTER 2: Deductive Reasoning
|
|
- Tamsin Barber
- 6 years ago
- Views:
Transcription
1 GEOMETRY CHAPTER 2: Deductive Reasoning NAME Page 1 of 34
2 Section 2-1: If-Then Statements; Converses Conditional Statement: If hypothesis, then conclusion. hypothesis conclusion converse conditional statement in which the and the are switched. If, then. counterexample an example that refutes or disproves a hypothesis, proposition, or theorem. For #1 to 5, underline the hypothesis once and the conclusion twice of each conditional. 1. VW = XY implies. 2. K is the midpoint of only if JK = KL. 3. n > 8 only if n is greater than I ll dive if you dive. 5. If a = b, then a + c = b + c. If the condition or converse is false, provide a counterexample. 6. If today is Thursday, then tomorrow is Friday. Hypothesis: Conclusion: Converse: Conditional: True or False Converse: True or False Page 2 of 34
3 7. If you have a 95, then you have an A. Hypothesis: Conclusion: Converse: Conditional: True or False Converse: True or False 8. If Lisa lives in Langhorne, then she lives in PA. Hypothesis: Conclusion: Converse: Conditional: True or False Converse: True or False 9. If x = 5, then 4x = 20. Hypothesis: Conclusion: Converse: Conditional: True or False Converse: True or False 5. If x = 2, then x 2 = 4. Hypothesis: Conclusion: Converse: Conditional: True or False Converse: True or False Page 3 of 34
4 Bi Conditional: if and only if or iff if and only if. Ex. Congruent angles are angles that have congruent measures. Ex. Obtuse angles are angles with measures between 90 and 180. Page 4 of 34
5 Page 5 of 34
6 Section 2-2: Properties of Algebra Properties of Equality Addition Property Subtraction Property Multiplication Property Division Property Substitution Property Reflexive Property Symmetric Property Transitive Property If a = b and c = d, then. If a = b and c = d, then. If a = b, then. If a = b and c 0, then. If a = b, then either a or b may be for the other in any equation (or inequality). a = If a = b, then. If a = b and b = c, then. Properties of Congruence Reflexive Property D Symmetric Property If, then. If D E, then. Transitive Property If and, then. If D E and E F, then. Properties of Real Numbers Commutative Property Associative Property Distributive Property a + b =, ab = a + (b + c) =, a(bc) = a(b + c) = Page 6 of 34
7 Examples: Justify each step with a Property from Algebra. Follow the example below: Given: 4x 5 = 2 Prove: x = Statements Reasons 1. 4x 5 = 2 1. Given 2. 4x = 3 2. Addition Property of Equality 3. x = 3. Division Property of Equality 1. Given: Prove: a = Statements Reasons Given 2. 3a = a = Given: 11 Prove: z = 40 Statements Reasons Given 2. z + 7 = z = Page 7 of 34
8 3. Given: 15y + 7 = 12 20y Prove: y = Statements Reasons 1. 15y + 7 = 12 20y 1. Given 2. 35y + 7 = y = y = Given: x 2 = Prove: x = 6 Statements Reasons 1. x 2 = 1. Given 2. 5(x 2) = 2x x 10 = 2x x 10 = x = x = 6 6. Page 8 of 34
9 2.2 Substitution Property Practice I. 1. a = b + c 1. Given d = e + f 2. a = d 2. Given Substitution II. 1. a = b + c 1. Given d = e + f 2. b + c = e + f 2. Given Substitution (Diagram is for III. And IV.) D E F III. IV. V. A B C 1. DF = AC 1. Given 2. DE + EF = 2. AB + BC = Substitution 1. DE + EF = AB + BC 1. Given 2. DE + EF = 2. AB + BC = Substitution 1. WOY XOZ 1. Given 2. m WOY = m 1 + m 2 2. m XOZ = m 3 + m Substitution W O X Y Z Page 9 of 34
10 Page 10 of 34
11 Section 2-3: Proving Theorems Midpoint Theorem: If M is the midpoint of, then AM = AB and MB = AB. A M B Definition of a Midpoint: If M is the midpoint of, then or AM = MB. Angle Bisector Theorem: If is the bisector of ABC, then m ABX = m ABC and m XBC = m ABC. A X B C Definition of Angle Bisector: If is the bisector of ABC, then ABX XBC or m ABX = m XBC. Reasons Used in Proofs Page 11 of 34
12 Directions Be sure to mark your diagrams as you work. 1. Given: AB = CD Prove: AC = BD A B C D STATEMENTS REASONS 1. AB = CD BC = BC AB + BC = CD + BC AB + BC = AC; CD + BC = BD AC = BD Given: AC = BD Prove: AB = CD A B C D STATEMENTS REASONS Given Segment Addition Postulate Substitution Property Reflexive Property of Equality Subtraction Property of Equality Page 12 of 34
13 3. Given: m 1 = m 2 Prove: m ABD = m CBE A C 1 D B 2 E STATEMENTS REASONS Given 2. m CBD = m CBD Addition Property of Equality 4. m 1 + m CBD = m ABD 4. m 2 + m CBD = m CBE Substitution Property 4. Given: m ABD = m CBE Prove: m 1 = m 2 A C 1 D B 2 E STATEMENTS REASONS 1. m ABD = m CBE Angle Addition Postulate Substitution Property 4. m CBD = m CBD Page 13 of 34
14 Sections 2-1 to Given: m CAT = m BAG Prove: m 1 = m 2 STATEMENTS REASONS 1. m CAT = m BAG m CAT = m 1 + m 3; 2. m BAG = m 2 + m Substitution Property 4. m 3 = m m 1 = m Given: ZP = LC; ZI = OC Prove: IP = LO STATEMENTS REASONS Given Segment Addition Postulate 3. ZI + IP = LO + OC 3. Substitution Property 4. ZI = OC 4. Given Subtraction Property of Equality Page 14 of 34
15 3. Given: m 1 = m 2; m 3 = m 4 Prove: m XYZ = m TUV STATEMENTS REASONS Given 2. m 1 + m 3 = m 2 + m Substitution Property 4. Given: MA = TH Prove: MT = AH STATEMENTS REASONS 1. MA = TH AT = AT Addition Property of Equality Segment Addition Postulate Page 15 of 34
16 Page 16 of 34
17 Page 17 of 34
18 Review Sheet for Quiz 2-1 to If m 1 = 110, then the angle is obtuse. a. hypothesis - b. conclusion - c. Is the statement True or False? If False, give a counterexample. d. converse - e. Is the converse True or False? If False, give a counterexample. 2. If bisects KAT, then m KAL = m LAT. a. hypothesis - b. conclusion - c. Is the statement True or False? If False, give a counterexample. d. converse - e. Is the converse True or False? If False, give a counterexample. Page 18 of 34
19 For questions 3-13, complete the next questions by supplying the letter of the reason. (A) Addition Property of Equality (B) Multiplication Property of Equality (C) Definition of Angle Bisector (D) Angle Addition Postulate (E) Substitution Property (F) Segment Addition Postulate (G) Subtraction Property of Equality (H) Angle Bisector Theorem (I) Reflexive Property (J) Midpoint Theorem (K) Transitive Property (L) Definition of Midpoint Name the definition, postulate, or theorem that justifies each statement. 3. If g = h, then g + k = h + k. 4. MN = MN 5. If x + y = z and x = 6, then 6 + y = z. 6. If PQ = QR and QR = ST, then PQ = ST. 7. If x 5 = 20, then x = If 2 (m 2) = 110, then m 2 = 55. For questions, 9-13, use the diagram to the right. 9. m 3 + m 4 = m MPQ. J 10. If H is the midpoint of, then HM = HJ. 11. If bisects QPM, then m 3 = m QPM. H Q 12. If Q is the midpoint of, then PQ = PJ. 13. PQ + QJ = PJ. M 4 3 P Page 19 of 34
20 COMPLETE THE FOLLOWING PROOF. Given: WX = YZ Prove: WY = XZ W X Y Z STATEMENTS REASONS XY = XY WX + XY = XY + YZ WX + XY = WY 4. XY + YZ = XZ Given: WY = XZ Prove: WX = YZ W X Y Z STATEMENTS REASONS Page 20 of 34
21 Section 2-4: Special Pairs of Angles Complementary Angles: two angles whose measures have a sum of 90. Each angle is called a complement of the other. Supplementary Angles: two angles whose measures have a sum of 180. Each angle is called a supplement of the other Vertical Angles: two angles formed by a pair of intersecting lines that are directly across from one another. **Vertical Angle Theorem: Vertical angles are congruent. Examples: Give the complement and the supplement of each angle measure b Page 21 of 34
22 (3x 5) Classify each statement as true or false. 4. If m A + m B + m C = 180, then A, B, C are supplementary. 5. Vertical angles have the same measure. 6. If 1 and 2 are vertical angles, m 1 = 2x + 18, and m 2 = 3x + 4, then x = 14. Complete with always, sometimes, or never. 7. Vertical angles have a common vertex. 8. Two right angles are complementary. 9. Right angles are vertical angles. 10. Angles A, B, and C are complementary. 11. Vertical angles have a common supplement. 12. If A and B are supplementary, find the value of x, m A, and m B. m A = x + 16, m B = 2x Find the value of x. 70 Page 22 of 34
23 Page 23 of 34
24 Page 24 of 34
25 Page 25 of 34
26 Section 2-5: Perpendicular Lines Definition of Perpendicular Lines: two lines that intersect to form right angles (90º angles.) If two lines are perpendicular, then they form congruent adjacent angles. If two lines form congruent adjacent angles, then the lines are perpendicular. The exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary. If two angles are supplements of congruent angles (or the same angle), then the two angles are congruent. If two angles are complements of congruent angles (or the same angle, then the two angles are congruent. Page 26 of 34
27 Examples:. Use the diagram to classify each statement as true or false. 1. AB EF 2. CGB is a right angle. 3. CGA is a right angle. 4. m DGB = EGC and EGA are complements. C E A G B F D 6. DGF is complementary to DGA. 7. EGA is complementary DGF. Complete with always, sometimes, or never. 8. Perpendicular lines lie in the same plane. 9. Two lines are perpendicular if and only if they form congruent adjacent angles. 10. Perpendicular lines form 60 angles. 11. If the exterior sides of two adjacent angles are perpendicular, then the angles are supplementary. 12. If a pair of vertical angles are supplementary, the lines forming the angles are perpendicular. Page 27 of 34
28 Page 28 of 34
29 Page 29 of 34
30 Page 30 of 34
31 Page 31 of 34
32 Review Sheet for Chapter 2 Test Use the conditional statement to answer questions #1-5. Conditional Statement: If three points are coplanar, then they are collinear. 1. hypothesis: 2. conclusion: 3. Is the conditional statement True or False? (If false, give a counterexample.) 4. Converse: 5. Is the converse True or False? (If false, give a counterexample.) In the diagram,. Name: Y V W X T U 6. two acute vertical angles 7. two congruent supplementary angles 8. two adjacent complementary angles 9. two right angles 10. two obtuse vertical angles Page 32 of 34
33 (A) Addition Property of Equality (L) Subtraction Property of Equality (B) Multiplication Property of Equality (M) Angle Addition Postulate (C) Definition of Angle Bisector (N) Segment Addition Postulate (D) Angle Bisector Theorem (O) Definition of Midpoint (E) Substitution Property (P) Midpoint Theorem (F) Reflexive Property (Q) Transitive Property (G) Definition of complementary angles (R) Definition of perpendicular lines (H) Definition of supplementary angles (S) Vertical angles are congruent (I) If two lines are perpendicular, then they form congruent adjacent angles. (J) If two lines form congruent adjacent angles, then the lines are perpendicular. (K) If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary. For questions #11-20, name the definition, property, postulate, or theorem that justifies each statement. Given: X is the midpoint of ; bisects CXB A D 1 2 X C E B 11. CX + XD = CD 12. m AXC = m DXB 13. AX = XB 14. m 1 = m m 1 = ( )m CXB 16. XE = XE 17. AX = ( ) AB 18. m AXE + m EXB = m BXE + m EXA = m BXA 20. m CXB = m AXD Page 33 of 34
34 In questions #21 25, angles. 21. m ADF = 22. m EDC = 23. m CDB = 24. m ADB = and m 1 = 49. Find the measures of the following G E 1 D F C A B 25. m EDB = In questions #21-23,. Use the given information to find the value of x. 26. m 1 = (7x) ; m 4 = (x + 42) x = 27. m 3 = (4x + 35) ; m 4 = (x + 5) x = 28. m 4 = (7x + 13) ; m EAD = (10x 3) x = 29. m 1 = (x + 1) ; m FAC = (9x 11) x = 30. m 2 = (x + 1) x = 31. COMPLETE THE FOLLOWING PROOF. Given: m CAT = m BAG Prove: m 1 = m 3 A C 1 C E A D F 4 B 2 3 T B G STATEMENTS REASONS Given Angle Addition Postulate 3. m 1 + m 2 = m 2 + m Subtraction Property of Equality Page 34 of 34
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 informationProofs 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 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 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 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 informationLesson. 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 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 informationConditional 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 informationGeometry Honors: Midterm Exam Review January 2018
Name: Period: The midterm will cover Chapters 1-6. Geometry Honors: Midterm Exam Review January 2018 You WILL NOT receive a formula sheet, but you need to know the following formulas Make sure you memorize
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 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 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 informationChapter 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 informationGeometry Honors Review for Midterm Exam
Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers
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 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 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 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 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 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 informationQuestion 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 informationGeometry 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 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 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 information1-2 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 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 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 information2.8 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 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 informationANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1
ANSWERS STUDY GUIDE FOR THE FINAL EXAM CHAPTER 1 N W A S Use the diagram to answer the following questions #1-3. 1. Give two other names for. Sample answer: PN O D P d F a. Give two other names for plane.
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 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 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 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 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 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 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 informationNotes: 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 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 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 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 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 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 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 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 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 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 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 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 informationGeometry Arcs and Chords. Geometry Mr. Austin
10.2 Arcs and Chords Mr. Austin Objectives/Assignment Use properties of arcs of circles, as applied. Use properties of chords of circles. Assignment: pp. 607-608 #3-47 Reminder Quiz after 10.3 and 10.5
More informationA plane can be names using a capital cursive letter OR using three points, which are not collinear (not on a straight line)
Geometry - Semester 1 Final Review Quadrilaterals (Including some corrections of typos in the original packet) 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that
More informationChapter 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 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 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 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 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 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 informationGEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent?
GEO REVIEW TEST #1 Name: Date: 1. In which quadrilateral are the diagonals always congruent? (1) rectangle (3) rhombus 4. In the accompanying diagram, lines AB and CD intersect at point E. If m AED = (x+10)
More informationQuestions. Exercise (1)
Questions Exercise (1) (1) hoose the correct answer: 1) The acute angle supplements. angle. a) acute b) obtuse c) right d) reflex 2) The right angle complements angle whose measure is. a) 0 b) 45 c) 90
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 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 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 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 informationReview 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 information1-2 Measuring and Constructing Segments
1-2 Measuring and Constructing Segments Lesson Presentation Lesson Quiz Objectives Use length and midpoint of a segment. Construct midpoints and congruent segments. Vocabulary coordinate midpoint distance
More informationGeometry 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 informationGEO 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 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 informationChapters 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 informationGeometry Arcs and Chords. Geometry Mr. Peebles Spring 2013
10.2 Arcs and Chords Geometry Mr. Peebles Spring 2013 Bell Ringer: Solve For r. B 16 ft. A r r 8 ft. C Bell Ringer B 16 ft. Answer A r r 8 ft. C c 2 = a 2 + b 2 Pythagorean Thm. (r + 8) 2 = r 2 + 16 2
More informationName 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 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 informationGeometry - Semester 1 Final Review Quadrilaterals
Geometry - Semester 1 Final Review Quadrilaterals 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that apply. a. Plane L b. Plane ABC c. Plane DBC d. Plane E e. Plane
More information*Please do not write on these worksheets. Show all diagrams, work, and answers on your own piece of paper*
Geometry Homework Worksheets: Chapter 1 *Please do not write on these worksheets. Show all diagrams, work, and answers on your own piece of paper* HW#1: Problems #1-10 For #1-4, choose the best answer
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 informationNozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'
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 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 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 Practice Midterm
Class: Date: Geometry Practice Midterm 2018-19 1. If Z is the midpoint of RT, what are x, RZ, and RT? A. x = 19, RZ = 38, and RT = 76 C. x = 17, RZ = 76, and RT = 38 B. x = 17, RZ = 38, and RT = 76 D.
More informationMath 3 Review Sheet Ch. 3 November 4, 2011
Math 3 Review Sheet Ch. 3 November 4, 2011 Review Sheet: Not all the problems need to be completed. However, you should look over all of them as they could be similar to test problems. Easy: 1, 3, 9, 10,
More informationInt. Geometry Unit 2 Test Review 1
Int. Geometry Unit Test Review irections -: Use the diagram to determine if the angles are vertical, adjacent, supplementary, complementary, or a linear pair. Write all that apply.. and. and 6 0. 8 and
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 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 informationChapter 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 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 informationCommon Core Math 3. Proofs. Can you find the error in this proof "#$%&!!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!
Common Core Math 3 Proofs Can you find the error in this proof "$%& a = b'()$&2 = 1 *+,+$-$%+.. /$,0)%. " a = b $%&'( ) a 2 = ab = a 2 - b 2 = ab - b 2? (a + b)(a - b) = b(a - b) @ (a + b) = b B a + a
More informationProperties of Isosceles and Equilateral Triangles
Properties of Isosceles and Equilateral Triangles In an isosceles triangle, the sides and the angles of the triangle are classified by their position in relation to the triangle s congruent sides. Leg
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
EOCT Practice Items 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B'
More informationWrite a 2-column or flow chart proof for the following:
Proofs Study Guide Write a 2-column or flow chart proof for the following: If 6 = a + 2, ten a = 16. 4 Write a 2-column or flow chart proof for the following: If 9x 7 = 7, ten x = 0. Write a 2-column or
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 informationDistance. Warm Ups. Learning Objectives I can find the distance between two points. Football Problem: Bailey. Watson
Distance Warm Ups Learning Objectives I can find the distance between two points. Football Problem: Bailey Watson. Find the distance between the points (, ) and (4, 5). + 4 = c 9 + 6 = c 5 = c 5 = c. Using
More informationTriangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.
Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?
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 A Exam Review, Chapters 1-6 Final Exam Review Name
Final Exam Review Name Hr. Final Exam Information: The Final Exam consists of a Multiple-Choice Section and an Open-Response Section. You may not use notes of any kind on the Final Exam. This Exam Review
More informationFive-Minute Check (over Lesson 2 7) CCSS Then/Now Postulate 2.10: Protractor Postulate Postulate 2.11: Angle Addition Postulate Example 1: Use the
Five-Minute Check (over Lesson 2 7) CCSS Then/Now Postulate 2.10: Protractor Postulate Postulate 2.11: Angle Addition Postulate Example 1: Use the Angle Addition Postulate Theorems 2.3 and 2.4 Example
More informationCommon Core Math 3. Can you find the error in this proof. Unit 2B - Proofs
Common Core Math 3 Unit 2B - Proofs Can you find the error in this proof "$%& a = b'()$& 2 = 1 *+,+$-$%+.. /$,0)%. " a = b $%&'( ) a 2 = ab = a 2 - b 2 = ab - b 2? (a + b)(a - b) = b(a - b) @ (a + b) =
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 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 information