CHAPTER Vocabulary 2

1 Copyright by Holt, Rinehart and rights table contains important Vocabulary terms from CHAPTER 2. As you workthrough the CHAPTER , fill in the page number, definition, and a clarifying ExampleCopyright by Holt, Rinehart and rights table contains important Vocabulary terms from CHAPTER 2. As you workthrough the CHAPTER , fill in the page number, definition, and a clarifying statement that can bewritten in the form p ifand only if q. The part of aconditional statementfollowing the word statement that can bewritten in the form if p,then q, where p is thehypothesis and q is statement that isbelieved to be statement formedby both exchangingand negating thehypothesis andconclusion of aconditional example that provesthat a conjecture orstatement is process of usinglogic to part of aconditional statementfollowing the word figure is a triangle ifand only if it is a three-sided x 1 5, then x x 1 5, then x conclusionA sequence beginswith the terms 2, 4, 6, 8,10.

2 A reasonableconjecture is that thenext term in thesequence is : If n 1 3,then n : If n 2, then n 1 : All monthshave 30 :October has 31 squares a ABCDis x 1 5, then x TermPageDefinitionClarifying ExampleCopyright by Holt, Rinehart and rights 2 Vocabulary CONTINUED inductivereasoninglogicallyequivalentsta tementsnegationpolygonquadrilateraltheor emtriangletruth valueTermPageDefinitionClarifying ExampleCopyright by Holt, Rinehart and rights 2 Vocabulary CONTINUED inductivereasoninglogicallyequivalentsta tementsnegationpolygonquadrilateraltheor emtriangletruth value74838298981109882 The process ofreasoning that a rule orstatement is truebecause specific casesare that havethe same truth negation ofstatement p is not p, written as ~ closed plane figureformed by three ormore segments suchthat each segmentintersects exactly twoother segments only attheir endpoints and notwo segments with acommon endpoint four-sided statement that hasbeen three-sided statement can have atruth value of true (T) orfalse (F).

3 3, 6, 9, 12, 15, ..Multiples of 3 make upthe pattern. The nextmultiple is m A 67 , then Ais Ais not acute, thenm A 67 .Statement:x 3 Negation:x 3 Theorem 2-6-1: If twoangles form a linearpair, then they today is Sunday, thentomorrow is truth value is true(T).TermPageDefinitionClarifying ExampleChapter Review2 CHAPTERC opyright by Holt, Rinehart and rights Using Inductive Reasoning to Make ConjecturesFind the next term in each , 12, 18, .. , April, July, .. table shows the score on a reactiontime test given to five students in both themorning and afternoon. The lower scoresindicate a faster reaction time. Use the tableto make a conjecture about reaction that the conjecture If a number is a multiple of 5, then it is an oddnumber is false by finding a Conditional the hypothesis and conclusion of the conditional statement Twoangles whose sum is 90 are complementary angles .Write a conditional statement from each of the angle that measures 90 is a right Morning Review2 CHAPTERC opyright by Holt, Rinehart and rights Using Inductive Reasoning to Make ConjecturesFind the next term in each , 12, 18.

4 , April, July, .. table shows the score on a reactiontime test given to five students in both themorning and afternoon. The lower scoresindicate a faster reaction time. Use the tableto make a conjecture about reaction that the conjecture If a number is a multiple of 5, then it is an oddnumber is false by finding a Conditional the hypothesis and conclusion of the conditional statement Twoangles whose sum is 90 are complementary angles .Write a conditional statement from each of the angle that measures 90 is a right an angle measurers90 , then the angle is aright a number is an evennumber, then it is an : Two angles whose sum is 90 .Conclusion: The angles are complementary.(10, 20, 30) are counterexamplesThe scores for the afternoon testwere lower, indicating a fasterreaction time as compared to themorning Morning by Holt, Rinehart and rights if each conditional is true. If false, give a an angle has a measure of 90 , then it is an acute 6x 2 4x 12, then x the converse, inverse, and contrapositive of the statement If a numberis divisible by 4, then it is an even number.

5 Find the truth value of Using Deductive Reasoning to Verify Conjectures if the following conjecture is valid by the Law of : Nicholas can watch 30 minutes of television if he cleans his roomfirst. Nicholas cleans his : Nicholas watches 30 minutes of if the following conjecture is valid by the Law of : If a point Ais on MN , then it divides MN into MA and AN . If MA AN then Ais the midpoint of MN .Conjecture: If a point is on MN , then Ais the midpoint of MN .2-4 Biconditional Statements and the conditional If two angles are complementary, then the sum of themeasures is 90 , write the converse and a biconditional :Biconditional statement:converse:truth value:inverse:truth value:contrapositive:truth value: CHAPTER 2 REVIEW CONTINUEDC opyright by Holt, Rinehart and rights if each conditional is true. If false, give a an angle has a measure of 90 , then it is an acute 6x 2 4x 12, then x the converse, inverse, and contrapositive of the statement If a numberis divisible by 4, then it is an even number.

6 Find the truth value of Using Deductive Reasoning to Verify Conjectures if the following conjecture is valid by the Law of : Nicholas can watch 30 minutes of television if he cleans his roomfirst. Nicholas cleans his : Nicholas watches 30 minutes of if the following conjecture is valid by the Law of : If a point Ais on MN , then it divides MN into MA and AN . If MA AN then Ais the midpoint of MN .Conjecture: If a point is on MN , then Ais the midpoint of MN .2-4 Biconditional Statements and the conditional If two angles are complementary, then the sum of themeasures is 90 , write the converse and a biconditional :If the sum of the measures of two angles is 90 , then thetwo angles are statement:Two angles are complementary if and only ifthe sum of their measures is 90 .No, it is not :If a number is an even number, then it is divisible by 4truth value:Finverse:If a number is not divisible by 4, then it is not an value:Fcontrapositive:If a number is not an even number, then it is notdivisible by value:TFalse,x 7 False, it is a right 2 REVIEW CONTINUEDC opyright by Holt, Rinehart and rights if the biconditional A point divides a segment into twocongruent segments if and only if the point is the midpoint of the segment, is true.

7 If false, give a Algebraic ProofSolve each equation. Write a justification for each 3 4 2017. x2 5 Identify the property that justifies each 1 m 2, so m 1 PQ , so PQ MN m 3 m 2 m CDand CD EF, A m Aso AB EF2-6 Geometric in the blanks to complete the two-column :m MOP m ROP 90 1 4 Prove: 2 3 Proof:ORMPQ1234 NCHAPTER 2 REVIEW CONTINUEDC opyright by Holt, Rinehart and rights if the biconditional A point divides a segment into twocongruent segments if and only if the point is the midpoint of the segment, is true. If false, give a Algebraic ProofSolve each equation. Write a justification for each 3 4 2017. x2 5 Identify the property that justifies each 1 m 2, so m 1 PQ , so PQ MN m 3 m 2 m CDand CD EF, A m Aso AB EF2-6 Geometric in the blanks to complete the two-column :m MOP m ROP 90 1 4 Prove: 2 3 Proof:ORMPQ1234 NReflexive Property ofEqualityTransitive Property ofEqualitySymmetric Property ofCongruenceAddition Property ofEquality 2 x2 5( 2),Mult.

8 Prop. ofEqualityx 10 Simplify. 4 4, of Equality3m 24,Simplify. 33m 234 of Equalitym 8 Simplify. 3 3 Sub. Equalitym 5 2 REVIEW CONTINUEDC opyright by Holt, Rinehart and rights the given plan to write a two-column : MOP NOQP rove: MON POQPlan: By the definition of anglecongruence, m MOP m the angle addition postulate to show that m MOP m MON m NOP. Show a similar statement for NOQ. Use the given fact to equatem MON m NOPand m POQ m subtraction property ofequality allows you to show m MON m POQ. Use the definition ofcongruent triangles to establish what needs to be 2 REVIEW CONTINUEDS tatementsReasons1. Transitive Property of Subtraction Property of m 1 m 1 m 2 m MOPm 3 m 4 m m 1 m 2 m 3 m by Holt, Rinehart and rights the given plan to write a two-column : MOP NOQP rove: MON POQPlan: By the definition of anglecongruence, m MOP m the angle addition postulate to show that m MOP m MON m NOP.

9 Show a similar statement for NOQ. Use the given fact to equatem MON m NOPand m POQ m subtraction property ofequality allows you to show m MON m POQ. Use the definition ofcongruent triangles to establish what needs to be 2 REVIEW CONTINUEDS tatementsReasons1. of Congruent Addition Postulate4. Transitive Property of Subtraction Property of MOP m ROP 90 1 42. m 1 m 1 m 2 m MOPm 3 m 4 m 1 m 2 m 3 m 45. m 1 m 2 m 3 m 2 m 3 StatementsReasonsGivenDefinition of Congruent AnglesAngle Addition PostulateTransitive Property of EqualitySubtraction Property of EqualityDefinition of Congruent Angles MOP NOQm MOP m NOQm MON m NOP m MOPm POQ m NOP m NOQm MON m NOP m POQ m NOPm MON m POQ MON POQC opyright by Holt, Rinehart and rights Flowchart and Paragraph ProofsUse the given two-column proof to write the : 1 4 Prove: 1 is supplementary to flowchart paragraph proofCHAPTER 2 REVIEW CONTINUEDS tatementsReasons1.

10 Given2. Definition of Congruent Angles3. Linear Pair Theorem4. Definition of SupplementaryAngles5. Transitive Property of Equality6. Substitution Property of Equality7. Subtraction Property of Equality8. Substitution Property of Equality9. Definition of Supplementary s 1. 1 42. m 1 m 43. 1 & 2 are supplementary. 3 & 4 are 1 m 2 180 m 3 m 4 180 5. m 1 m 2 m 3 m 46. m 1 m 2 m 3 m 17. m 2 m 38. m 1 m 3 180 9. 1 is supplementary to by Holt, Rinehart and rights Flowchart and Paragraph ProofsUse the given two-column proof to write the : 1 4 Prove: 1 is supplementary to flowchart paragraph proofThe m 1 m 4, as given andusing the definition of congruentangles. Because of the Linear Pairtheorem, 1 and 2 aresupplementary, as are 3 and , by the transitiveproperty of equality, m 1 m 2 m 3 m 4 180 .Additionally, since m 1 m 4,m 1 m 2 m 3 m the Subtraction Property ofEquality, m 2 m 3. Thatimplies that by substitution,m 1 m 3 180.