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NAME DATE2-1PERIODWord Problem PracticeInductive Reasoning and Conjecture1. RAMPS Rodney is rolling marbles downa ramp. Every second that passes, hemeasures how far the marbles travel. Herecords the information in the tableshown below.Second1st2nd3rd4thDistance (cm)20601001404. MEDALS Barbara is in charge of theaward medals for a sporting event. Shehas 31 medals to give out to variousindividuals on 6 competing teams. Sheasserts that at least one team will endup with more than 5 medals. Do youbelieve her assertion? If you do, try toexplain why you think her assertion istrue, and if you do not, explain how shecan be wrong.Make a conjecture about how far themarble will roll in the fifth second.2. PRIMES A prime number is a numberother than 1 that is divisible by onlyitself and 1. Lucille read that primenumbers are very important incryptography, so she decided to find asystematic way of producing primenumbers. After some experimenting,she conjectured that 2n 1 is a primefor all whole numbers n 1. Find acounterexample to this conjecture.PATTERNS For Exercises 5–7, use thefollowing information.The figure shows a sequence of squareseach made out of identical square tiles.3. GENEOLOGY Miranda is developinga chart that shows her ancestry. Shemakes the three sketches shown below.The first dot represents herself. Thesecond sketch represents herself andher parents. The third sketchrepresents herself, her parents, andher grandparents.6. Make a conjecture about the list ofnumbers you started writing in youranswer to Exercise 5.Sketch what you think would be thenext figure in the sequence.7. Make a conjecture about the sum of thefirst n odd numbers.Chapter 210Glencoe GeometryCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.5. Starting from zero tiles, how many tilesdo you need to make the first square?How many tiles do you have to addto the first square to get the secondsquare? How many tiles do you haveto add to the second square to get thethird square?

NAME DATE2-2PERIODWord Problem PracticeLogic1. HOCKEY Carol asked John if hishockey team won the game last nightand if he scored a goal. John said “yes.”Carol then asked Peter if he or Johnscored a goal at the game. Peter said“yes.” What can you conclude aboutwhether or not Peter scored?4. CIRCUITS In Earl’s house, the diningroom light is controlled by two switchesaccording to the following table. ( p owndownoffNovels455Poetry672838Plays26s5. How many people said they like allthree types of literature?6. How many like to read poetry?7. What percentage of the people who likeplays also like novels and poetry?18Glencoe GeometryCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Chapter 2rLightREADING For Exercises 5–7, use thefollowing information.Two hundred people were asked what kindof literature they like to read. They couldchoose among novels, poetry, and plays. Theresults are shown in the Venn diagram.3. VIDEO GAMES Harold is allowed toplay video games only if he washes thedishes or takes out the trash. However,if Harold does not do his homework, heis not allowed to play video games underany circumstance. Complete the truthtable.p: Harold has washed the dishesq: Harold has taken out the trashr: Harold has done his homeworks: Harold is allowed to play video gamesqSwitch BIf up and on are considered true anddown and off are considered false, writean expression that gives the truth valueof the light as a function of the truthvalues of the two switches.2. CHOCOLATE Nash has a bag ofminiature chocolate bars that come intwo distinct types: dark and milk.Nash picks a chocolate out of the bag.Consider these statements:p: the chocolate bar is dark chocolateq: the chocolate bar is milk chocolateIs the following statement true?pSwitch A

NAME DATE2-3PERIODWord Problem PracticeConditional StatementsVENN DIAGRAMS For Exercises 5–8,use the following information.Jose made this Venn diagram to show howrectangles, squares, and rhombi are related.(A rhombus is a quadrilateral with foursides of equal length.)Rectangles2. PARALLELOGRAMS Clark says thatbeing a parallelogram is equivalentto being a quadrilateral with equalopposite angles. Write his statementin if-then form.Squares1. TANNING Maya reads in a paper thatpeople who tan themselves underthe Sun for extended periods are atincreased risk of skin cancer. From thisinformation, can she conclude that shewill not increase her risk of skin cancerif she avoids tanning for extendedperiods of time?RhombiLet Q be a quadrilateral. For each problemtell whether the statement is true or false.If it is false, provide a counterexample.5. If Q is a square, then Q a rectangle.6. If Q is not a rectangle, then Q is not arhombus.7. If Q is a rectangle but not a square,then Q is not a rhombus.4. MEDICATION Linda’s medicine bottlesays “If you are pregnant, then youcannot take this medicine.” What are theinverse, converse, and the contrapositiveof this statement?Chapter 28. If Q is not a rhombus, then Q is not asquare.26Glencoe GeometryCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.3. AIR TRAVEL Ulma is waiting to boardan airplane. Over the speakers shehears a flight attendant say “If you areseated in rows 10 to 20, you may nowboard.” What are the inverse, converse,and the contrapositive of this statement?

NAME DATE2-4PERIODWord Problem PracticeDeductive Reasoning1. SIGNS Two signs are posted on ahaunted house.5ALLOWEDNO ONEUNDER 8ALLOWEDWITHOUT APARENTCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Inside the haunted house, you find achild with his parent. What can youdeduce about the age of the child basedon the house rules?2. LOGIC As Laura’s mother rushed offto work, she quickly gave Laura someinstructions. “If you need me, try mycell . . . if I don’t answer it means I’m ina meeting, but don’t worry, the meetingwon’t last more than 30 minutes andI’ll call you back when it’s over.” Laterthat day, Laura needed her mother, buther mother was stuck in a meetingand couldn’t answer the phone. Lauraconcludes that she will have to wait nomore than 30 minutes before she getsa call back from her mother. What lawof logic did Laura use to draw thisconclusion?LAWS For Exercises 5 and 6, use thefollowing information.The law says that if you are under 21,then you are not allowed to drink alcoholicbeverages and if you are under 18, thenyou are not allowed to vote. For eachproblem give the possible ages of theperson described or state that the personcannot exist.5. John cannot drink wine legally but isallowed to vote.3. MUSIC Composer Ludwig vanBeethoven wrote 9 symphonies and 5piano concertos. If you lived in Viennain the early 1800s, you could attend aconcert conducted by Beethoven himself.Write a valid conclusion to thehypothesis If Mozart could not attend aconcert conducted by Beethoven, . . .Chapter 26. Mary cannot vote legally but can drinkbeer legally.33Glencoe GeometryLesson 2-4NO ONEUNDER4. DIRECTIONS Hank has anappointment to see a financial advisoron the fifteenth floor of an officebuilding. When he gets to the building,the people at the front desk tell himthat if he wants to go to the fifteenthfloor, then he must take the red elevator.While looking for the red elevator, aguard informs him that if he wants tofind the red elevator he must find thereplica of Michelangelo’s David. Whenhe finally got to the fifteenth floor, hisfinancial advisor greeted him asking,“What did you think of theMichelangelo?” How did Hank’s financialadvisor conclude that Hank must haveseen the Michelangelo statue?

NAME DATE2-5PERIODWord Problem PracticePostulates and Paragraph Proofs1. ROOFING Noel and Kirk are building anew roof. They wanted a roof with twosloping planes that meet along a curvedarch. Is this possible?4. POINTS Carson claims that a line canintersect a plane at only one point anddraws this picture to show hisreasoning.PZoe thinks it is possible for a line tointersect a plane at more than one point.Who is correct? Explain.2. AIRLINES An airline company wants toprovide service to San Francisco, LosAngeles, Chicago, Dallas, WashingtonD. C., and New York City. The companyCEO draws lines between each pair ofcities in the list on a map. No three ofthe cities are collinear. How many linesdid the CEO draw?3. TRIANGULATION A sailor spots awhale through her binoculars. Shewonders how far away the whale is, butthe whale does not show up on the radarsystem. She sees another boat in thedistance and radios the captain askinghim to spot the whale and record itsdirection. Explain how this addedinformation could enable the sailor topinpoint the location of the whale.Under what circumstance would thisidea fail?5. What is the maximum number of linesegments that can be drawn betweenpairs among the 16 points?6. When the owner finished the picture, hefound that his company was split intotwo groups, one with 10 people and theother with 6. The people within a groupwere all friends, but nobody from onegroup was a friend of anybody from theother group. How many line segmentswere there?Chapter 240Glencoe GeometryCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.FRIENDSHIPS For Exercises 5 and 6,use the following information.A small company has 16 employees. Theowner of the company became concernedthat the employees did not know each othervery well. He decided to make a picture ofthe friendships in the company. He placed16 points on a sheet of paper in such away that no 3 were collinear. Each pointrepresented a different employee. He thenasked each employee who their friendswere and connected two points with a linesegment if they represented friends.

NAME DATE2-6PERIODWord Problem Practice1. DOGS Jessica and Robert each own thesame number of dogs. Robert and Gailalso own the same number of dogs.Without knowing how many dogs theyown, one can still conclude that Jessicaand Gail each own the same number ofdogs. What property is used to makethis conclusion?4. FIGURINES Pete and Rhonda paintfigurines. They can both paint 8figurines per hour. One day, Pete worked6 hours while Rhonda worked 9 hours.How many figurines did they paint thatday? Show how to get the answer usingthe Distributive Property.Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.2. MONEY Lars and Peter both have thesame amount of money in their wallets.They went to the store together anddecided to buy some cookies, splittingthe cost equally. After buying thecookies, do they still have the sameamount of money in their wallets? Whatproperty is relevant to help you decide?AGE For Exercises 5 and 6, use thefollowing information.William’s father is eight years older than4 times William’s age. William’s father is36 years old.5. Let x be William’s age. Translate thegiven information into an algebraicequation involving x.4. MANUFACTURING A companymanufactures small electroniccomponents called diodes. Each diodeis worth 1.50. Plant A produced 4,443diodes and Plant B produced 5,557diodes. The foreman was asked whatthe total value of all the diodes was.The foreman immediately responded“ 15,000.” The foreman would not havebeen able to compute the value soquickly if he had to multiply 1.50 by4,443 and then add this to the resultof 1.50 times 5,557. Explain how youthink the foreman got the answer soquickly?6. Fill in the missing steps andjustifications for each step in findingthe value of x.Algebraic StepsProperties4x 8 36Original equationSubtractionProperty4x 284x28 44SubstitutionPropertyChapter 247Glencoe GeometryLesson 2-6Algebraic Proof

NAME DATE2-7PERIODWord Problem PracticeProving Segment Relationships1. FAMILY Maria is 11 inches shorterthan her sister Nancy. Brad is 11 inchesshorter than his brother Chad. If Mariais shorter than Brad, how do the heightsof Nancy and Chad compare? What ifMaria and Brad are the same height?4. NEIGHBORHOODS Karla, John, andMandy live in three houses that are onthe same line. John lives between Karlaand Mandy. Karla and Mandy live a mileapart. Is it possible for John to be a milefrom both Karla and Mandy?2. DISTANCE Martha and Laura live1,400 meters apart. A library is openedbetween them and is 500 meters fromMartha.LIGHTS For Exercises 5 and 6, use thefollowing information.Five lights, A, B, C, D, and E, are lined upin a row. The middle light is the midpointof the second and fourth light and also themidpoint of the first and last light.500 metersMarthaLibraryLaura5. Draw a figure to illustrate the situation.1400 metersHow far is the library from Laura? D and A E .Given: C is the midpoint of BProve: AB DE3. LUMBER Byron works in a lumberyard. His boss just cut a dozen planksand asked Byron to double check thatthey are all the same length. The plankswere numbered 1 through 12. Byrontook out plank number 1 and checkedthat the other planks are all the samelength as plank 1. He concluded thatthey must all be the same length.Explain how you know plank 7 andplank 10 are the same length eventhough they were never directlycompared to each other?Chapter 2StatementReason1. C is the midpoint 1. Givenof BD and A E .2. BC CD and2.543. AC AB BC,CE CD DE3.4. AB AC BC4.5.5. SubstitutionProperty6. DE CE CD6.7.7.Glencoe GeometryCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.6. Complete this proof.

NAME DATE2-8PERIODWord Problem PracticeProving Angle RelationshipsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.1. ICOSAHEDRA For a school project,students are making a gianticosahedron, which is a large solid withmany identical triangular faces. John isassigned quality control. He must makesure that the measures of all the anglesin all the triangles are the same as eachother. He does this by using a precuttemplate and comparing the cornerangles of every triangle to the template.How does this assure that the angles inall the triangles will be congruent toeach other?4. PAINTING Students are painting theirrectangular classroom ceiling. They wantto paint a line that intersects one of thecorners as shown in the figure.15 They want the painted line to make a15 angle with one edge of the ceiling.Unfortunately, between the line and theedge there is a water pipe making itdifficult to measure the angle. Theydecide to measure the angle to the otheredge. Given that the corner is a rightangle, what is the measure of the otherangle?2. VISTAS If you look straight ahead at ascenic point, you can see a waterfall. Ifyou turn your head 25º to the left, youwill see a famous mountain peak. If youturn your head 35º more to the left, youwill see another waterfall. If you arelooking straight ahead, through howmany degrees must you turn your headto the left in order to see the secondwaterfall?For Exercises 5–7, use the followinginformation.Clyde looks at a building from point E. AEC has the same measure as BED.AEBC3. TUBES A tube with a hexagonal crosssection is placed on the floor.D5. The measure of AEC is equal to thesum of the measures of AEB and whatother angle?120 1What is the measure of 1 in the figuregiven that the angle at one corner of thehexagon is 120 ?6. The measure of BED is equal to thesum of the measures of CED and whatother angle?7. Is it true that m AEB is equal tom CED?Chapter 261Glencoe GeometryLesson 2-8Cross section of pipe

NAME DATE3-1PERIODWord Problem PracticeParallel Lines and Transversals1. FIGHTERS Two fighter aircraft flyat the same speed and in the samedirection leaving a trail behind them.Describe the relationship between thesetwo trails.4. NEIGHBORHOODS John, Georgia, andPhillip live nearby each other as shownin the map.HighStreetPhilliptreetySGeorgiaLow StreetBaJohnDescribe how their corner anglesrelate to each other in terms ofalternate interior, alternate exterior,corresponding, consecutive interior, orvertical angles.2. ESCALATORS An escalator at ashopping mall runs up several levels.The escalator railing can be modeled bya straight line running past horizontallines that represent the floors.Floor AFloor Bthe following figure.Floor CHighSDescribe the relationships of these lines.treetPhilliptreetySBaJohn3. DESIGN Carol designed the pictureframe shown below. How many pairsof parallel segments are there amongvarious edges of the frame?GeorgiaLow Street5. Connor lives at the angle that forms analternate interior angle with Georgia’sresidence. Add Connor to the map.6. Quincy lives at the angle that forms aconsecutive interior angle with Connors’residence. Add Quincy to the map.Chapter 310Glencoe GeometryCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.MAPPING For Exercises 5 and 6, useEscalator Railing

NAME DATE3-2PERIODWord Problem PracticeAngles and Parallel Lines1. RAMPS A parking garage ramp risesto connect two horizontal levels of aparking lot. The ramp makes a 10 angle with the horizontal. What is themeasure of angle 1 in the figure?4. PODIUMS A carpenter is building apodium. The side panel of the podium iscut from a rectangular piece of wood.1116 RampLevel 2Level 12. BRIDGES A double decker bridge hastwo parallel levels connected by anetwork of diagonal girders. One of thegirders makes a 52 angle with thelower level as shown in the figure. Whatis the measure of angle 1?SECURITY For Exercises 5 and 6, usethe following information.An important bridge crosses a river at a keylocation. Because it is so important, roboticsecurity cameras are placed at the locationsof the dots in the figure. Each robot canscan x degrees. On the lower bank, it takes4 robots to cover the full angle from theedge of the river to the bridge. On the upperbank, it takes 5 robots to cover the fullangle from the edge of the river to thebridge.1geupper bank115 Bridlower bank5. How are the angles that are coveredby the robots at the lower and upperbanks related? Derive an equation thatx satisfies based on this relationship.

Chapter 1 10 Glencoe Geometry Word Problem Practice Points, Lines, and Planes . Lesson 1-3 05-56 Geo-01-873958 4/3/06 6:29 PM Page 25. Chapter 1 33 Glencoe Geometry . 1-6 1. ARCHITECTURE In the Uffizi gallery in Florence, Italy, there is a room filled with paintings by Bronzino called the