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NameLESSON2-1DateClassPractice BUsing Inductive Reasoning to Make ConjecturesFind the next item in each pattern.1. 100, 81, 64, 49, . . .2. 363. Alabama, Alaska, Arizona, . . .4. west, south, east, . . .ArkansasnorthComplete each conjecture.5. The square of any negative number ispositive6. The number of segments determined by n points is.n(n 1)2.Show that each conjecture is false by finding a counterexample.7. For any integer n, n 3 0.Possible answers: zero, any negative number8. Each angle in a right trianglehas a different measure. 9. For many years in the United States, each bank printed its own currency. The varietyof different bills led to widespread counterfeiting. By the time of the Civil War, asignificant fraction of the currency in circulation was counterfeit. If one Civil Warsoldier had 48 bills, 16 of which were counterfeit, and another soldier had 39 bills,13 of which were counterfeit, make a conjecture about what fraction of bills werecounterfeit at the time of the Civil War.One-third of the bills were counterfeit.Make a conjecture about each pattern. Write the next two items.10. 1, 2, 2, 4, 8, 32, . . .11. Each item, starting with the,third, is the product of the twoThe dot skips over one vertexpreceding items; 256, 8192.in a clockwise direction.Copyright by Holt, Rinehart and Winston.All rights reserved.001 082 Go07an HPB.indd 88Holt Geometry10/9/06 11:35:49 AMProcess Black

NameLESSON2-2DateClassPractice BConditional StatementsIdentify the hypothesis and conclusion of each conditional.1. If you can see the stars, then it is night.2. A pencil writes well if it is sharp.You can see the stars.It is A pencil is sharp.The pencil writes well.Write a conditional statement from each of the following.3. Three noncollinear points determine a plane.If three points are noncollinear, then they determine a plane.4.FruitIf a food is a kumquat, then it is a fruit.KumquatsDetermine if each conditional is true. If false, give a counterexample.5. If two points are noncollinear, then a right triangle contains one obtuse angle.true6. If a liquid is water, then it is composed of hydrogen and oxygen.true7. If a living thing is green, then it is a plant.false; sample answer: a frog8. “If G is at 4, then GH is 3.” Write the converse,inverse, and contrapositive of this(statement. Find the truth value of each. 5Converse:Inverse:Contrapositive:05If GH is 3, then G is at 4; falseIf G is not at 4, then GH is not 3; falseIf GH is not 3, then G is not at 4; trueThis chart shows a small part of the Mammaliaclass of animals, the mammals. Write a conditionalto describe the relationship between each given pair.-AMMALS2ODENTS0RIMATES,EMURS!PESIf an animal is a primate, then it is a mammal.lemurs and rodents Sample answer: If an animal is a lemur, then it is not a rodent.rodents and apes Sample answer: If an animal is a rodent, then it is not an ape.If an animal is an ape, then it is a mammal.apes and mammals9. primates and mammals10.11.12.Copyright by Holt, Rinehart and Winston.All rights reserved.9Holt Geometry

NameLESSON2-3DateClassPractice BUsing Deductive Reasoning to Verify ConjecturesTell whether each conclusion is a result of inductive or deductive reasoning.1. The United States Census Bureau collects data on the earnings of American citizens.Using data for the three years from 2001 to 2003, the bureau concluded that the nationalaverage median income for a four-person family was 43,527.inductive reasoning2. A speeding ticket costs 40 plus 5 per mi/h over the speed limit. Lynne mentionsto Frank that she was given a ticket for 75. Frank concludes that Lynne was driving7 mi/h over the speed limit.deductive reasoningDetermine if each conjecture is valid by the Law of Detachment.››3. Given: If m ABC m CBD, then BC bisects ABD. BC bisects ABD.Conjecture: m ABC m CBD.invalid4. Given: You will catch a catfish if you use stink bait. Stuart caught a catfish.invalidConjecture: Stuart used stink bait.5. Given: An obtuse triangle has two acute angles. Triangle ABC is obtuse.Conjecture: Triangle ABC has two acute angles.validDetermine if each conjecture is valid by the Law of Syllogism.6. Given: If the gossip said it, then it must be true. If it is true, thensomebody is in big trouble.Conjecture: Somebody is in big trouble because the gossip said it.valid7. Given: No human is immortal. Fido the dog is not human.invalidConjecture: Fido the dog is immortal.8. Given: The radio is distracting when I am studying. If it is 7:30 P.M.on a weeknight, I am studying.Conjecture: If it is 7:30 P.M. on a weeknight, the radio is distracting.validDraw a conclusion from the given information.9. Given: If two segments intersect, then they arenot parallel.If two segments arenot parallel, then they could be perpendicular. EF and MN intersect.EF and MN could be perpendicular.10. Given: When you are relaxed, your blood pressure is relatively low. If you aresailing, you are relaxed. Becky is sailing.Becky’s blood pressure is relatively low.Copyright by Holt, Rinehart and Winston.All rights reserved.10Holt Geometry

NameDateLESSON2-4ClassPractice BBiconditional Statements and DefinitionsWrite the conditional statement and converse within each biconditional.1. The tea kettle is whistling if and only if the water is boiling.Conditional:Converse:If the tea kettle is whistling, then the water is boiling.If the water is boiling, then the tea kettle is whistling.2. A biconditional is true if and only if the conditional and converse are both true.If a biconditional is true, then the conditional and converse are bothtrue.If the conditional and converse are both true, then the biconditional is true.Conditional:Converse:For each conditional, write the converse and a biconditional statement.3. Conditional: If n is an odd number, then n 1 is divisible by 2.Converse:Biconditional:If n 1 is divisible by 2, then n is an odd number.n is an odd number if and only if n 1 is divisible by 2.4. Conditional: An angle is obtuse when it measures between 90 and 180 .Converse: Ifan angle measures between 90 and 180 , then the angle is obtuse.Biconditional: An angle is obtuse if and only if it measures between 90 and 180 .Determine whether a true biconditional can be written from eachconditional statement. If not, give a counterexample.5. If the lamp is unplugged, then the bulb does not shine.No; sample answer: The switch could be off.6. The date can be the 29th if and only if it is not February.No; possible answer: Leap years have a Feb. 29th.Write each definition as a biconditional.7. A cube is a three-dimensional solid with six square faces.A figure is a cube if and only if it is a three-dimensional solid with sixsquare faces.8. Tanya claims that the definition of doofus is “her younger brother.”A person is a doofus if and only if the person is Tanya’s younger brother.Copyright by Holt, Rinehart and Winston.All rights reserved.11Holt Geometry

NameLESSON2-5DateClassPractice BAlgebraic ProofSolve each equation. Show1 (a 10) 31.51 (a 10) 5( 3)55a 10 15a 10 10 15 10a –25[]all your steps and write a justification for each step.2. t 6.5 3t 1.3t 6.5 t 3t 1.3 t(Mult. Prop. of )6.5 2t 1.3(Simplify.)6.5 1.3 2t 1.3 1.3(Subtr. Prop. of ) 7.8 2t(Simplify.)2t7.8 223.9 tt 3.9(Subtr. Prop. of )(Simplify.)(Add. Prop. of )(Simplify.)(Div. Prop. of )(Simplify.)(Symmetric Prop. of )3. The formula for the perimeter P of a rectangle with length ᐉ and width w is1 feet.P 2(ᐉ w). Find the length of the rectangle shown here if the perimeter is 92Solve the equation for ᐉ and justify each step. Possible answer:P 2( w)1)1 2( 19421 2 21922(Given)7 2 (Simplify.)(Subst. Prop. of )2 7 (Div. Prop. of )1 321 32(Simplify.)2(Distrib. Prop.)1 21 2 21 21 (Subtr. Prop. of )92222211–4 ft(Symmetric Prop. of )Write a justification for each step.7X 34.2X 6() 3X 3 *HJ HI IJ7x 3 (2x 6) (3x 3)7x 3 5x 37x 5x 62x 6x 3Seg. Add. Post.Subst. Prop. of Simplify.Add. Prop. of Subtr. Prop. of Div. Prop. of Identify the property that justifies each statement.5. m n, so n m.6. ABC ABCSymmetric Prop. of Reflexive Prop. of 7. KL LK8. p q and q 1, so p 1.Reflexive Prop. of Copyright by Holt, Rinehart and Winston.All rights reserved.Transitive Prop. of or Subst.12Holt Geometry

NameDateClassPractice BLESSON2-6Geometric ProofWrite a justification for each step.Given: AB EF, B is the midpointof AC ,and E is the midpoint of DF .&% !"1. B is the midpoint of AC ,and E is the midpoint of DF .#Given2. AB BC , and DE EF .Def. of mdpt.3. AB BC, and DE EF.Def. of segmentsSeg. Add. Post.4. AB BC AC, and DE EF DF.5. 2AB AC, and 2EF DF.Subst.6. AB EFGiven7. 2AB 2EFMult. Prop. of 8. AC DFSubst. Prop. of Def. of segments9. AC DFFill in the blanks to complete the two-column proof.10. Given: HKJis a straight angle.›KI bisects HKJ.Prove: IKJ is a right angle.( *)Proof:Statements1. a. HKJ is a straight angle.2. m HKJ 180 ›3. c.KI bisects HKJReasons1. Given2. b.Def. of straight 3. Given4. IKJ IKH4. Def. of bisector5. m IKJ m IKH5. Def. of 6. d.m IKJ m IKH m HKJ6. Add. Post.7. 2m IKJ 180 7. e. Subst. (Steps8. m IKJ 90 8. Div. Prop. of 9. IKJ is a right angle.9. f.Copyright by Holt, Rinehart and Winston.All rights reserved.132, 5, 6)Def. of right Holt Geometry

NameLESSON2-7DateClassPractice BFlowchart and Paragraph Proofs1. Use the given two-column proof to write a flowchart proof.Given: 4 3Prove: m 1 m 2 StatementsReasons1. 1 and 4 are supplementary, 2 and 3 are supplementary.1. Linear Pair Thm.2. 4 32. Given3. 1 23. Supps. Thm.4. m 1 m 24. Def. of 'IVEN AND ARE SUPPLEMENTARY AND ARE SUPPLEMENTARY ,IN 0AIR 4HM 3UPPS 4HM M M EF OF2. Use the given two-column proof to write a paragraph proof.Given: AB CD, BC DE!"# %Prove: C is the midpoint of AE .StatementsReasons1. AB CD, BC DE1. Given2. AB BC CD DE2. Add. Prop. of 3. AB BC AC, CD DE CE3. Seg. Add. Post.4. AC CE4. Subst.5. AC CE5. Def. of segs.6. Def. of mdpt.6. C is the midpoint of AE .It is given that AB CD and BC DE, so by the Addition Property ofEquality, AB BC CD DE. But by the Segment Addition Postulate,AB BC AC and CD DE CE. Therefore substitution yieldsAC CE. By the definition of congruent segments, AC CE and thusC is the midpoint of AE by the definition of midpoint.Copyright by Holt, Rinehart and Winston.All rights reserved.14Holt Geometry

NameLESSON3-1DateClassPractice BLines and AnglesFor Exercises 1–4, identify each of the following in the figure.%1. a pair of parallel segments" !&plane ABC 储 plane DEFIn Exercises 5–10, give one example ofeach from the figure.XY18273645Z6. parallel linesline zCF EF#4. a pair of parallel planes5. a transversalAB and CF are skew.2. a pair of skew segments3. a pair of perpendicular segmentsSampleanswers:BE 储 AD7. corresponding angleslines x and ySample answer: 1 and 38. alternate interior angles9. alternate exterior angles10. same-side interior anglesSample answer: 2 and 6Sample answer: 1 and 5Sample answer: 2 and 3Use the figure for Exercises 11–14. The figure shows autility pole with an electrical line and a telephone line.The angled wire is a tension wire. For each angle pairgiven, identify the transversal and classify the anglepair. (Hint: Think of the utility pole as a line for theseproblems.)11. 5 and 643651tension wire2electricallinetelephonelineutility pole12. 1 and 4transv.: utility pole; same-sidetransv.: tension wire; alternateinterior anglesexterior angles13. 1 and 214. 5 and 3transv.: telephone line;transv.: utility pole; alternatecorresponding anglesinterior anglesCopyright by Holt, Rinehart and Winston.All rights reserved.15Holt Geometry

NameLESSON3-2DateClassPractice BAngles Formed by Parallel Lines and TransversalsFind each angle measure.2133 119 147 1. m 1119 2. m 2#X ! (8X 34) "(5X 2) %&97 3. m ABC62 4. m DEFComplete the two-column proof to show that same-side exterior anglesare supplementary.5. Given: p qProve: m 1 m 3 180 Proof:12 3PQStatements1. p q2. a.Reasons1. Givenm 2 m 3 180 3. 1 24. c.m 1 m 25. d.m 1 m 3 180 2. Lin. Pair Thm.3. b.Corr. Post.4. Def. of 5. e.Subst.6. Ocean waves move in parallel lines toward the shore.The figure shows Sandy Beaches windsurfing acrossseveral waves. For this exercise, think of Sandy’s wakeas a line. m 1 (2x 2y) and m 2 (2x y) .Find x and y.x 15y 40Copyright by Holt, Rinehart and Winston.All rights reserved.116270 Holt Geometry

NameLESSON3-3DateClassPractice BProving Lines ParallelUse the figure for Exercises 1–8. Tell whether lines m and nmust be parallel from the given information. If they are, stateyour reasoning. (Hint: The angle measures may change foreach exercise, and the figure is for reference only.)1. 7 3MN1 82 73 64 52. m 3 (15x 22) , m 1 (19x 10) ,x 8m 储 n; Conv. of Alt. Int. Thm.m 储 n; Conv. of Corr. Post.3. 7 64. m 2 (5x 3) , m 3 (8x 5) ,x 14m and n are parallel if and only ifm 储 n; Conv. of Same-Sidem 7 90 .Int. Thm.5. m 8 (6x 1) , m 4 (5x 3) , x 96. 5 7m 储 n; Conv. of Corr. Post.m and n are not parallel.7. 1 58. m 6 (x 10) , m 2 (x 15) m 储 n; Conv. of Alt. Ext. Thm.m and n are not parallel.9. Look at some of the printed letters in a textbook. The small horizontal andvertical segments attached to the ends of the letters are called serifs. Most of theletters in a textbook are in a serif typeface. The letters on this page do not haveserifs, so these letters are in a sans-serif typeface. (Sans means “without” in French.)The figure shows a capital letter A with serifs.Use the given informationto write aparagraph proof that the serif, segment HI , is parallel to segment JK .Given: 1 and 3 are supplementary.Prove: HI JK*(1 23 )Sample answer: The given information states that 1 and 3 aresupplementary. 1 and 2 are also supplementary by the Linear PairTheorem. Therefore 3 and 2 must be congruent by theCongruentSupplements Theorem. Since 3 and 2 are congruent, HI and JKare parallel by the Converse of the Corresponding Angles Postulate.Copyright by Holt, Rinehart and Winston.All rights reserved.17Holt Geometry

NameDateClassPractice BLESSON3-4Perpendicular LinesFor Exercises 1–4, name the shortest segment from the point to the line andwrite an inequality for x. (Hint: One answer is a double inequality.)1.2.03.5' (X11X 421*P

LESSON 1-5 Practice B Using Formulas in Geometry Use the figures for Exercises 1–3. 1. Find the perimeter of triangle A. 12 ft FT FT FT! FT H " 2. Find the area of triangle A. 6 ft 2 3. Triangle A is identical to triangle B. Find the height h of triangle B. 2.4 ft