Notes #35: Inequalities and Reasoning (Sections 6.1 and 6.2)
|
|
- Brianne Nelson
- 6 years ago
- Views:
Transcription
1 Geometry Rules! Chapter 6 Notes Notes #35: Inequalities and Reasoning (Sections 6.1 and 6.) lgebraic Inequalities in if/then form: (Hint: given that the if statement is true, can we say that the then statement must be true?) If it is not true, provide a counterexample (explain why). 1.) If c 3 < 5, then c < 8..) If d 3 > 4, then d > 5. 3.) If x > 4, then x > 3. 4.) If x > 3, then x > 4. Inequalities in Geometry: Whole > Part 5.) Fill in the blank with <, >, or = Y a) Y + Y b) Y c) Y 6.) Can you conclude each statement? (yes/no) X a) m OX = ½ m O b) m OX + m XO = m O c) m O > m XO d) m O < 90 e) m XO > m OX f) m O > m OX O Inverses/Contrapositives: Original: If Mrs. Spragg has a hermit crab, then she has a pet. If p ( ), then q ( ). Contrapositive: If not q ( ), then not p ( ).
2 Converse: - - If q, then p. Inverse: If not p, then not q. Write the contrapositive, converse, and inverse of each. State whether each is true or false: (T/F) 7.) Original: If I live in Encinitas, then I live in California. Contrapositive: (If not q, then not p.) Converse: (If q, then p) Inverse: (If not p, then not q.) statement and its are logically equivalent. statement s converse and its are logically equivalent. Deductive Reasoning: Consider the given statements as true and write it in if, then form. What can you conclude from each additional piece of information? (It might help to write its logically equivalent contrapositive, too.) 8.) ll US Presidents are at least 35 years old. Original: If, then. Contrapositive: If, then. a) Tracy Smith is 38 years old. b) George ush is the president.
3 c) Mr. Rich is not the president. d) Mr. King is years old ) ll runners are athletes. Original: If, then. Contrapositive: If, then. a) Leroy is a runner b) Pam is not an athlete c) Sara is an athlete d) Jim is not a runner lgebra Practice: Simplify (factor first, when possible!) 10.) 1x 18x ) 4ab 16ab ) c d 4c+ 4d 13.) 6x 8y ) x x + x x ) x + 4x x+ x
4 Notes #36: Indirect Proof, Proofs by Contradiction (Section 6.3) Indirect proofs are used to prove statements that are difficult or impossible to prove using accepted theorems, postulates, and definitions. Indirect proof, or proof by contradiction, proves a statement by demonstrating that its (demonstrating that the contrapositive is true). 1.) Given: Scott hit a single and a home run on Friday. Prove: Scott played in a baseball game on Friday. ssume temporarily that Scott did not. Then he could not have. However, this contradicts the given that. Therefore, our assumption was wrong, and. Recipe for an indirect proof: ssume temporarily (the opposite of the conclusion) (Make logical conclusions until you reach a problem) However, this contradicts the given because (explain the problem) Therefore, my assumption is false and (the original conclusion must be true) Write the first sentence of an indirect proof for each of the following statements:.) If m<x = 60, then m< = ) If m = n, then n p.
5 Write an indirect proof for each: ) Given: diagram Prove: X isn t a median of C 5 X 8 C ssume temporarily that. Then, X would be the, and by, =. However, this contradicts the given because Therefore, my assumption is false, and. 5.) Given: C, m< = 110 Prove: < is not a right angle 6.) Given: Jon enters the house with a dry umbrella. Prove: It is not raining outside.
6 lgebra Practice: Simplify (factor first, when possible!) ) 8x + 10x+ 3 8x + x 3 8.) x 4 7x x ) 6x 15x 9 4x 6x 4 10.) 5x 10x x 10x 11.) 3 x x x x 5x 4 1.) (-m 3 n 5 )(5mn ) 13.) (4x 3 y ) 14.) (-j 4 k ) 3 (5jk 3 ) 15.) (x + 4)
7 Notes #37: Triangle Inequalities and Ratios (Sections 6.4 and 7.1) The largest angle of a triangle is opposite the side of the triangle. The smallest angle of a triangle is opposite the side of the triangle. Name the largest and smallest angle of the triangle: (not necessarily drawn to scale) 1.).) a + 1 X Y C Largest: Smallest: a - 1 Z a Largest: Smallest: Name the longest and shortest side of the triangle: (not necessarily drawn to scale) 3.) 4.) 46 4 C Longest: Shortest: Z Shortest: Name the largest and smallest angle: (not necessarily drawn to scale) 5.) X 63 7 Y Longest: Largest: Smallest: Name the longest side: (not necessarily drawn to scale) 6.) S 48 Longest: R 55 T 5 65 U
8 The Triangle Inequality The sum of the lengths of of a triangle is greater than the length of the. When given three side lengths of a possible triangle, they can form a triangle if: (short side) + (short side) > (long side) Is it possible for a triangle to have sides with length: (Yes/No) 7) 8, 7, 6 8) 9, 9, 19 9), 3, 4 When given two side lengths of a triangle, the third side of the triangle must be between their difference and their sum. (length length) < third side < (length + length) The lengths of two sides of a triangle are given. The length of the third side must be greater than but less than. 10.) 3, 7 11.) 1, 19 1.) 3a, 4a +
9 lgebra Practice: Simplify (factor first, if possible!) ) (3a b 3 ) (-5a 3 b 6 ) 14.) (4d 5) 15.) (x y 3 ) + (3xy 4 )(5x 3 y ) 16.) 36 4x 6x + x i 17.) 9x 4x 9 8xy x + 3x 4x 1 + 3x x x x x Ratios: Comparing numbers with division 18.) Find each ratio: a) D:DC 8 C 6 b) m<:m<d 40 D c) D: Perimeter of CD 19.) If x = 5, y = 10, z = 3 find each ratio: a) x to y b) (x + z) to y c) x+ y 7z
10 Ratio word problems: - attach an x to each part of the ratio - write and solve an equation using these expressions ) The ratio of two complementary angles is 1:. Find each angle. 1.) The ratio of two supplementary angles is 7:. Find each angle.) The ratio of the angles of a triangle is :3:4. Find each angle. 3.) The ratio of the angles of a pentagon is :3:4:4:5. Find each angle.
11 Classwork #38: Chapter 6 Review Classify each if-then statement as True or False. 1. If x > 6, then x > 5.. If x> 1, then x> 13. Complete each statement by writing <, =, or >. 3. X X 4. C 5. C C 1 D 6. m 1 70 º 7. m 70º F E State whether each statement is True or False. Then write the (a) contrapositive, (b) converse, and (c) inverse and state whether each is True or False. T/F 8. If two lines do not intersect, then they are skew. (a) (contrapositive) (b) (converse) (c) (inverse) Complete the indirect proof: 9. Given: Quadrilateral CD, m = 80. Prove: CD is not a rectangle. ssume temporarily that. Then m = because. However, this contradicts the that. Therefore, was wrong and. 10. Is it possible for a triangle to have sides with the given lengths: (yes/no) (a), 4, 6 (b) 5, 5, The lengths of two sides of a triangle are given. The length of the third side must be greater than but less than. (a), 8 (b) b, b + 3
12 Name the longest and shortest side of the given figure: 13. Name the largest and the smallest side of the given triangle: O G 4x - 10 D S x + 10 x The angles of a triangle are in the ratio of :3:4. Find the angles. Simplify: 15. (3c 3 d 4 ) (-cd 5 ) 16. (4x 3) a + a 9a a a 18. m + 5m+ 3 m y 10y y+ 6 4y 36 15y 3 i 0. w w w w 1 6w w 1
13 HW #38: Study Guide (Sections , 7.1) Classify each if-then statement as True or False. If false, provide a counterexample. 1. If x > 6, then x > 3.. If x > 3, then x >. 3. If x> 15, then x> 17. Complete each statement by writing <, =, or >. X 4. X 5. C C 1 D 6. X C 7. m 1 75 º F E State whether each statement is True or False. Then write the (a) contrapositive, (b) converse, and (c) inverse. State whether each is True or False. T/F 8. If two lines do not intersect, then they are skew. (a) (b) (c) ccept the given statement as true. What can you conclude by using the given statement together with each additional statement? 9. Given: ll students love math. (a) randen is a student. (c) lan loves math. (b) Kim is not a student. (d) Jim does not love math. What is the first sentence of an indirect proof of the statement shown? 10. If = C, then DE = EF. 11. If m = 30, then m 30. Complete the indirect proof: 1. Given: Quadrilateral CD, m = 80. Prove: CD is not a square. ssume temporarily that. Then, m = because. However, this contradicts the because Therefore, was wrong and.
14 Is it possible for a triangle to have sides with the indicated lengths? (Yes/No) 13. 1,, , 4, The lengths of two sides of a triangle are given. The length of the third sides must be greater than but less than , a, a + 6 If the diagram was drawn to scale, name the largest and smallest angles. 17. In C, = 11, C = 1, and C = b R b Y 10 8 Z Largest: Smallest: Q b - 1 P Largest: Smallest: 1 3 Largest: Smallest: If the diagram was drawn to scale, name the shortest and longest sides. 0. In C, m< = 60, m< = 59, m<c = U x Longest: Shortest: Simplify: 6ab 3. 1ab x - T S Longest: Shortest: D 59 C Longest: Shortest: 4. x+ y for x= 3, y =, z = 1 z x Write and equation and solve: 5. The ratio of the angles of a triangle is 1:3:5. Find the angles. 6. The ratio of two complementary angles is 5:1. Find the angles. 7. The ratio of the angles of a pentagon is 6: 8: 9: 11: 11. Find the angles.
15 Simplify: (check that factoring!) ) (5m 3 n )(-4mn 8 ) 9.) (-3a 5 b ) 3 (ab 4 ) 30.) (6x 3 y ) (-3x 5 y ) 3 31.) 3a(a 3b) 3.) (x 1) 3 33.) x 5x+ 6 x 9 34.) x x 1 x 35.) 4mn p 8 36mnp ) 4x + x 3 6x 6 37.) m 6 m 3 4m+ 8 m ) 3 y + y 4y 8 y 1 i y + 3y+ 3y+ y 39.) 4c 1 c + 5c 3 6c 6 3c + 9c 3 40.) x x x x i x x x x
Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
5-5 Indirect Proof and and Inequalities in in One One Triangle Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up 1. Write a conditional from the sentence An isosceles triangle has two congruent
More informationTo use indirect reasoning to write proofs. Game A 1 2. Key Concept Writing an Indirect Proof
5-5 Indirect Common Core State Standards Extends G-CO.C.10 Prove theorems about triangles... MP 1, MP 3, MP Objective To use indirect reasoning to write proofs The goal of this game is to fill in the empty
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 informationGeometry Unit 2 Notes Logic, Reasoning and Proof
Geometry Unit Notes Logic, Reasoning and Proof Review Vocab.: Complementary, Supplementary and Vertical angles. Syllabus Objective:. - The student will justify conjectures and solve problem using inductive
More informationGeometry 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 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 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 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 informationAttendance Problems 1. Write a conditional from the sentence An isosceles triangle has two congruent sides.
Page 1! of 11! Attendance Problems 1. Write a conditional from the sentence An isosceles triangle has two congruent sides. 2. Write the contrapositive of the conditional If it is Tuesday, then John has
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 informationMidpoint M of points (x1, y1) and (x2, y2) = 1 2
Geometry Semester 1 Exam Study Guide Name Date Block Preparing for the Semester Exam Use notes, homework, checkpoints, quizzes, and tests to prepare. If you lost any of the notes, reprint them from my
More 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. Midterm Review
Geometry Midterm Review Class: Date: Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A plumber knows that if you shut off the water
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 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 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 informationChapter 2. Reasoning and Proof
Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9
More informationGeometry Semester 1 REVIEW
Name: Class: Date: ID: A Geometry Semester 1 REVIEW 1. The figure below is a rectangular shipping box. Name two different planes that contain BC. 2. Find BC. 3. The endpoints of GH are GÊ Ë Á 6, 9 ˆ and
More informationIntegrated Math II. IM2.1.2 Interpret given situations as functions in graphs, formulas, and words.
Standard 1: Algebra and Functions Students graph linear inequalities in two variables and quadratics. They model data with linear equations. IM2.1.1 Graph a linear inequality in two variables. IM2.1.2
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 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 informationSemester 1 Cumulative Summative Review Teacher: Date: B
GOMTRY Name: 2016-2017 Semester 1 umulative Summative Review Teacher: ate: To be prepared for your midterm, you will need to PRTI PROLMS and STUY TRMS from the following chapters. Use this guide to help
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 informationGeometry Semester 1 Exam Released
1. Use the diagram. 3. In the diagram, mlmn 54. L 5 1 4 3 2 Which best describes the pair of angles 1 and 4? (A) complementary (B) linear pair (C) supplementary (D) vertical 2. Use the diagram. E F A B
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 informationConditional Statements
Conditional Statements nalyze statements in if-then form. Write the converse, inverse, and contrapositive of if-then statements. Vocabulary conditional statement if-then statement hypothesis conclusion
More informationExamples: 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 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 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 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 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- involve reasoning to a contradiction. 1. Emerson is the tallest. On the assumption that the second statement is the true one, we get: 2. 3.
Math 61 Section 3.1 Indirect Proof A series of lessons in a subject that contradicted each other would make that subject very confusing. Yet, in reasoning deductively in geometry, it is sometimes helpful
More informationGeometry: CBA-I Review
Name: Period: ate: Geometry: 2013-2014 -I Review 1. Identify each construction. X 1 2 2. Identify the converse, inverse, contrapositive, and bi-conditional form of the statement given below. If a triangle
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 informationKEYSTONE ALGEBRA I REVIEW
1. Which graph represents a linear function 4. The faces of a cube are numbered from 1 to 6. If the cube is tossed once, what is the probability that a prime number or a number divisible by 2 is obtained
More information2.1 Start Thinking. 2.1 Warm Up. 2.1 Cumulative Review Warm Up
2.1 Start Thinking The statement If you are able to open the door, then the door is unlocked is always true. Write a statement you know to be true in the same if-then form. Support your statement with
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 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 informationGeometry Midterm Review Packet
Name: ate: lock: 2012 2013 Geometry Midterm Review Packet ue: 1/7/13 (for +5 on packet) 1/8/13 (for +3 on packet) 1/9/13 (for +2 on packet) 1/10/13 ( ay lasses) 1/11/13 ( ay lasses) The midterm will be
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 informationChapter 2. Reasoning and Proof
Chapter 2 Reasoning and Proof 2.1 Use Inductive Reasoning Objective: Describe patterns and use deductive reasoning. Essential Question: How do you use inductive reasoning in mathematics? Common Core: CC.9-12.G.CO.9
More informationName: Jan 2016 Semester1 Review Block: Date:
GOMTRY Name: Jan 2016 Semester1 Review lock: ate: To be prepared for your midterm, you will need to PRTI PROLMS and STUY TRMS from the following chapters. Use this guide to help you practice. Unit 1 (1.1
More informationIF-THEN STATEMENTS DAY 17
IF-THEN STATEMENTS DAY 17 DEDUCTIVE REASONING: The process of using orderly statements to make logical conclusions. IF-THEN STATEMENTS: CONDITIONAL STATEMENTS CONDITIONAL CONVERSE (FLIPPED CONDITIONAL)
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 informationGeo - CH2 Practice Test
Geo - H2 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the next item in the pattern 2, 3, 5, 7, 11,... a. 13 c. 15 b. 12 d. 17 2. The
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 informationLogic CHAPTER. 3.1 A Little Dash of Logic Two Methods of Logical Reasoning p. 101
CHAPTER Logic Riding a bicycle is a skill which, once learned, is rarely forgotten. What s more, bicycles are enough alike that if you can ride one bike, you can pretty much ride them all. This is an example
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 informationWork with a partner. Use dynamic geometry software. Draw any scalene ABC. a. Find the side lengths and angle measures of the triangle.
OMMON ORE Learning Standard HSG-O..0 6.5 Indirect Proof and Inequalities in One riangle Essential Question How are the sides related to the angles of a triangle? How are any two sides of a triangle related
More information5-1 Practice Form K. Midsegments of Triangles. Identify three pairs of parallel segments in the diagram.
5-1 Practice Form K Midsegments of Triangles Identify three pairs of parallel segments in the diagram. 1. 2. 3. Name the segment that is parallel to the given segment. 4. MN 5. ON 6. AB 7. CB 8. OM 9.
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 informationConditional Statements
2.1 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G.4.B Conditional Statements Essential Question When is a conditional statement true or false? A conditional statement, symbolized by p q, can be written as an
More informationNORTH 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 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 information2013 ACTM Regional Geometry Exam
2013 TM Regional Geometry Exam In each of the following choose the EST answer and record your choice on the answer sheet provided. To insure correct scoring, be sure to make all erasures completely. The
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 informationGeometry CP Semester 1 Review Packet. answers_december_2012.pdf
Geometry CP Semester 1 Review Packet Name: *If you lose this packet, you may print off your teacher s webpage. If you can t find it on their webpage, you can find one here: http://www.hfhighschool.org/assets/1/7/sem_1_review_packet
More informationProvide (write or draw) a counterexample to show that the statement is false.
Geometry SOL G.1 G.3a Study Guide Name: Date: Block: SHOW ALL WORK. Use another piece of paper as needed. SECTION 1: G.1 1. Provide (write or draw) a counterexample to show that the statement is false.
More informationLos Angeles Unified School District Periodic Assessments. Geometry. Assessment 2 ASSESSMENT CODE LA08_G_T2_TST_31241
Los Angeles Unified School District Periodic Assessments Assessment 2 2008 2009 Los Angeles Unified School District Periodic Assessments LA08_G_T2_TST_31241 ASSESSMENT ODE 1100209 The test items contained
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 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 informationG E O M E T R Y CHAPTER 2 REASONING AND PROOF. Notes & Study Guide CHAPTER 2 NOTES
G E O M E T R Y CHAPTER 2 REASONING AND PROOF Notes & Study Guide 2 TABLE OF CONTENTS CONDITIONAL STATEMENTS... 3 DEFINTIONS & BICONDITIONAL STATEMENTS... 6 DEDUCTIVE REASONING... 9 REASONING WITH PROPERTIES
More 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 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 informationMonday HW Answers a z = n = 2 5. angle: 40 degrees x = right isosceles 7. angle: 50 degrees x = work.
1. 34a 15 2. 2 3. z = 139 4. n = 2 5. angle: degrees x = 28 6. right isosceles 7. angle: degrees x = 6 Monday HW Answers. 1 Recap! A straight angle measures. A triangle always measures. A quadrilateral
More information3. Understand The Laws of Detachment and Syllogism 4. Appreciate a simple Ham Sandwich.
Lesson 4 Lesson 4, page 1 of 8 Glencoe Geometry Chapter 2.2 and 2.3 If-Then Statements & Deductive Reasoning By the end of this lesson, you should be able to 1. Write a statement in if-then Form. 2. To
More informationUnit 2: Geometric Reasoning Section 1: Inductive Reasoning
Unit 2: Geometric Reasoning Section 1: Inductive Reasoning Ex #1: Find the next item in the pattern. January, March, May,... Ex #2: Find the next item in the pattern. 7, 14, 21, 28, Ex #3: Find the next
More 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 informationName: Period: Date: Given: is the bisector of Draw JD and DL such that it makes triangle DJL. Then answer the question. a. 17 b. 73 c. 118 d.
Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which statement is not necessarily true? Name: Given: is the bisector of Draw JD and DL such that it makes
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 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 information4. Name the transformation needed to transform Figure A into Figure B, using one movement. l
Review 1 Use the following words to fill in the blank to make true sentences. translation rotation reflection 1. A is a transformation that slides a figure a given distance in a given direction. 2. A is
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 Practice Test Unit 2 Logic, Reasoning and Proof
Geometry Practice Test Unit 2 Logic, Reasoning and Proof Name: Date: Pd: Definitions (1-4) 1) Postulate 2) Deductive Reasoning 3) Inverse 4) Counterexample 5) State the hypothesis and conclusion of the
More information8th Grade. Slide 1 / 145. Slide 2 / 145. Slide 3 / 145. Pythagorean Theorem, Distance & Midpoint. Table of Contents
Slide 1 / 145 Slide 2 / 145 8th Grade Pythagorean Theorem, Distance & Midpoint 2016-01-15 www.njctl.org Table of Contents Slide 3 / 145 Proofs Click on a topic to go to that section Pythagorean Theorem
More informationName Geometry Common Core Regents Review Packet - 3. Topic 1 : Equation of a circle
Name Geometry Common Core Regents Review Packet - 3 Topic 1 : Equation of a circle Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( ) 1. The endpoints of a diameter
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 informationSEMESTER REVIEW 1: Chapters 1 and 2
Geometry Fall emester Review (13-14) EEER REVIEW 1: hapters 1 and 2 1. What is Geometry? 2. What are the three undefined terms of geometry? 3. Find the definition of each of the following. a. Postulate
More informationIndirect Proofs. State the hypothesis and the conclusion of the following conditional statement:
State the hypothesis and the conclusion of the following conditional statement: If it is cold outside, then Mr. Bates will wear a coat. Write your own conditional statement and state the hypothesis and
More informationYear 9 Term 3 Homework
Yimin Math Centre Year 9 Term 3 Homework Student Name: Grade: Date: Score: Table of contents 5 Year 9 Term 3 Week 5 Homework 1 5.1 Geometry (Review)................................... 1 5.1.1 Angle sum
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 informationLogic and Conditional Statements
Logic and Conditional Statements Organizing topic Reasoning and Proof Overview Students investigate symbolic form while working with conditional statements. Related Standard of Learning G.1 Objectives
More informationUNIT 1. Basics of Geometry. What is a pattern? Aug 20 11:14 AM. Jun 8 2:09 PM. Aug 20 10:46 AM. Aug 20 11:08 AM. 1.1 Finding and Describing Patterns
UNIT 1 Basics of Geometry 1.1 Finding and Describing Patterns What is a pattern? Jun 8 2:09 PM Aug 20 11:00 AM Aug 20 10:46 AM Aug 20 11:04 AM Let's Practice! Making predictions! Describe a pattern. 3.
More informationCorrelation: California State Curriculum Standards of Mathematics for Grade 6 SUCCESS IN MATH: BASIC ALGEBRA
Correlation: California State Curriculum Standards of Mathematics for Grade 6 To SUCCESS IN MATH: BASIC ALGEBRA 1 ALGEBRA AND FUNCTIONS 1.0 Students write verbal expressions and sentences as algebraic
More informationCh 3.2: Direct proofs
Math 299 Lectures 8 and 9: Chapter 3 0. Ch3.1 A trivial proof and a vacuous proof (Reading assignment) 1. Ch3.2 Direct proofs 2. Ch3.3 Proof by contrapositive 3. Ch3.4 Proof by cases 4. Ch3.5 Proof evaluations
More informationChapters Q1 Exam Practice Test
Chapters 1.1-3.3 Q1 Exam Practice Test Use the diagram to answer the following question(s). 1. What is another name for? L C E 2. What is another name for? O J 3. The figure below is a rectangular shipping
More informationPre-AP Geometry. True or False: 1. Points A, B, and D are collinear. 2. Points B, F, and H are coplanar. 3. Points H, B, D, and A are coplanar.
Pre-AP Geometry Unit 1 Test Review Name: Date: Period: True or False: 1. Points A, B, and D are collinear. 2. Points B, F, and H are coplanar.. Points H, B, D, and A are coplanar. 4. XV is the same as
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 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 informationGeometry 1 st Semester review Name
Geometry 1 st Semester review Name 1. What are the next three numbers in this sequence? 0, 3, 9, 18, For xercises 2 4, refer to the figure to the right. j k 2. Name the point(s) collinear to points H and
More informationRead ahead and use your textbook to fill in the blanks. We will work the examples together.
Math 1312 Section 1.1 : Sets, Statements, and Reasoning Read ahead and use your textbook to fill in the blanks. We will work the examples together. A set is any. hese objects are called the of the set.
More informationHONORS GEOMETRY CHAPTER 2 WORKBOOK
HONORS GEOMETRY CHAPTER 2 WORKBOOK FALL 2016 Chapter 2 Miscellaneous: The Structure of Geometry Vocabulary Definition Example Elements: 1. Deductive Structure Postulate (axiom) Example: Definitions Reversed:
More informationGeometry Test Unit 2 Logic, Reasoning and Proof
Geometry Test Unit 2 Logic, Reasoning and Proof Name: Date: Pd: Definitions (1-4) 1) Conditional Statement 2) Inductive Reasoning 3) Contrapositive 4) Logically equivalent statements 5) State the hypothesis
More informationDeductive reasoning is the process of reasoning from accepted facts to a conclusion. if a = b and c = d, c 0, then a/c = b/d
Chapter 2 Reasoning Suppose you know the following two statements are true. 1. Every board member read their back-up material 2. Tom is a board member You can conclude: 3. Tom read his back-up material.
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 information1 Implication and induction
1 Implication and induction This chapter is about various kinds of argument which are used in mathematical proofs. When you have completed it, you should know what is meant by implication and equivalence,
More information2.2 Analyze Conditional
2.2 Analyze Conditional Statements Goal p Write definitions as conditional statements. Your Notes VOCABULARY Conditional statement If-then form Hypothesis Conclusion Negation Converse Inverse Contrapositive
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 informationGeometry Chapter 2 2-3: APPLY DEDUCTIVE REASONING
Geometry Chapter 2 2-3: APPLY DEDUCTIVE REASONING Warm-up Any Definition can be written as a Biconditional Statement. For Warm-up: Write some of our past vocabulary terms as Biconditional statements. Terms:
More informationChapter 4 Reasoning and Proof Geometry
Chapter 4 Reasoning and Proof Geometry Name For 1 & 2, determine how many dots there would be in the 4 th and the 10 th pattern of each figure below. 1. 2. 3. Use the pattern below to answer the following:
More information