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Previous Next Page1 Lesson 2.3 • Finding the nth Term Name Period Date For Exercises 1–4, tell whether or not the rule is a linear function. 1. n 1 2 3 4 5 f(n) 8 15 22 29 36 3. n h(n) 1 !9 2 !6 3 4 n g(n) 4. 5 3 !2 2. 9 1 2 3 4 5 14 11 8 5 2 1 2 3 4 5 !1 !"12" 0 1 "" 2 n !"32" j(n) For Exercises 5 and 6, complete each table. 5. n 1 2 3 4 5 6. n 6 f(n) ! 7n " 12 1 2 3 4 5 6 g(n) ! "8n " 2 For Exercises 7–9, find the function rule for each sequence. Then find the 50th term in the sequence. 7. n f(n) 8. n g(n) 9. n h(n) 1 2 3 4 5 6 9 13 17 21 25 29 1 2 3 4 5 6 6 1 !4 !9 1 2 3 4 5 6 6.5 7 7.5 8 8.5 9 ... n ... 50 ... n ... 50 ... n ... 50 !14 !19 10. Find the rule for the number of tiles in the nth figure. Then find the number of tiles in the 200th figure. n 1 2 3 Number of tiles 1 4 7 4 5 ... n ... 200 11. Sketch the next figure in the sequence. Then complete the table. n 1 2 Number of segments and lines 2 6 Number of regions of the plane Discovering Geometry Practice Your Skills ©2003 Key Curriculum Press 3 4 ... n ... 50 4 CHAPTER 2 11 Name Class Practice 2-1 Date Page2 Conditional Statements Show that each conditional is false by finding a counterexample. 1. If it is 12:00 noon, then the sun is shining. 2. If the car is full of gas, then the engine will start. 3. If a number is divisible by 3, then it is odd. Write the converse of each conditional. 4. If you drink milk, then you will be strong. 5. If a rectangle has four sides the same length, then it is a square. 6. If you do not sleep, you will be tired. Write the converse of each statement. If the converse is true, write true; if it is not true, provide a counterexample. 7. If x - 4 = 22, then x = 26. 8. If ∆x∆ ! 0, then x ! 0. 9. If m2 is positive, then m is positive. 10. If y = 3, then 2y - 1 = 5. 11. If point A is in the first quadrant of a coordinate grid, then x ! 0. 12. If two lines have equal slopes, then the lines are parallel. © Pearson Education, Inc. All rights reserved. 13. If you are a twin, then you have a sibling. 14. Draw a Venn diagram to illustrate the statement in Exercise 13. Answer the following questions about the given quote. “If you like to shop, then visit the Pigeon Forge outlets in Tennessee.” 15. Identify the hypothesis and the conclusion. 16. What does the quote suggest about the Pigeon Forge outlets? 17. Write the converse of the conditional. 18. Is the converse of the conditional a true statement? Explain your reasoning. Answer the following questions about the billboard advertisement shown. 19. What does the billboard imply? 20. Write the advertisement slogan as a conditional statement. Train harder, run faster with SUSTAIN 21. Write the converse of the conditional statement from Exercise 20. Geometry Chapter 2 Lesson 2-1 Practice 1 Name Class Date Page3 Practice 2-2 Biconditionals and Definitions Each conditional statement is true. Consider each converse. If the converse is true, combine the statements and write them as a biconditional. 1. If two angles have the same measure, then they are congruent. 2. If 2x - 5 = 11, then x = 8. 3. If n = 17, then ∆n∆ = 17. 4. If a figure has eight sides, then it is an octagon. Write the two conditional statements that make up each biconditional. 5. A whole number is a multiple of 5 if and only if its last digit is either a 0 or a 5. 6. Two lines are perpendicular if and only if they intersect to form four right angles. 7. You live in Texas if and only if you live in the largest state in the contiguous United States. Explain why each of the following is not an acceptable definition. 8. An automobile is a motorized vehicle with four wheels. 9. A circle is a shape that is round. © Pearson Education, Inc. All rights reserved. 10. The median of a set of numbers is larger than the smallest number in the set and smaller than the largest number in the set. 11. Cricket is a game played on a large field with a ball and a bat. 12. A rectangle is a very pleasing shape with smooth sides and very rigid corners. Some figures that are piggles are shown below, as are some nonpiggles. piggles nonpiggles Tell whether each of the following is a piggle. 13. 2 14. Lesson 2-2 Practice 15. Geometry Chapter 2 Name Class Practice 2-3 Date Page4 Deductive Reasoning Use the Law of Detachment to draw a conclusion. 1. If the measures of two angles have a sum of 90°, then the angles are complementary. m&A + m&B = 90 2. If the football team wins on Friday night, then practice is canceled for Monday. The football team won by 7 points on Friday night. 3. If a triangle has one 90° angle, then the triangle is a right triangle. In !DEF, m&E = 90. Use the Law of Syllogism to draw a conclusion. 4. If you liked the movie, then you saw a good movie. If you saw a good movie, then you enjoyed yourself. 5. If two lines are not parallel, then they intersect. If two lines intersect, then they intersect at a point. 6. If you vacation at the beach, then you must like the ocean. If you like the ocean, then you will like Florida. If possible, use the Law of Detachment to draw a conclusion. If not possible, write not possible. © Pearson Education, Inc. All rights reserved. 7. If Robbie wants to save money to buy a car, he must get a part-time job. Robbie started a new job yesterday at a grocery store. 8. If a person lives in Omaha, then he or she lives in Nebraska. Tamika lives in Omaha. 9. If two figures are congruent, their areas are equal. The area of ABCD equals the area of PQRS. Use the Law of Detachment and the Law of Syllogism to draw conclusions from the following statements. 10. If it is raining, the temperature is greater than 32°F. If the temperature is greater than 32°F, then it is not freezing outside. It is raining. 11. If you live in Providence, then you live in Rhode Island. If you live in Rhode Island, then you live in the smallest state in the United States. Shannon lives in Providence. 12. If it does not rain, the track team will have practice. If the track team has practice, the team members will warm up by jogging two miles. It does not rain on Thursday. Geometry Chapter 2 Lesson 2-3 Practice 3 Name Class Date Page5 Practice 5-4 Inverses, Contrapositives, and Indirect Reasoning Identify the two statements that contradict each other. 1. I. ABCD is a trapezoid. II. AB 6 CD III. BC 6 AD A B D C A 2. I. AB ! BC II. m!A + m!B = 80 III. "ABC is isosceles. B C Write the negation of each statement. 3. The angle measure is 65. 4. Tina has her driver’s license. 5. The figure has eight sides. 6. The restaurant is not open on Sunday. 7. "ABC is not congruent to "XYZ. 8. m!Y ! 50 Write (a) the inverse and (b) the contrapositive of each statement. Give the truth value of each. © Pearson Education, Inc. All rights reserved. 9. If two triangles are congruent, then their corresponding angles are congruent. 10. If you live in Toronto, then you live in Canada. Write the first step of an indirect proof. 11. m!A = m!B 12. TUVW is a trapezoid. 13. LM intersects NO. 14. "FGH is equilateral. 15. It is sunny outside. 16. !D is not obtuse. 17. Write an indirect proof that m!A " 90. A C 4 B Lesson 5-4 Practice Geometry Chapter 5 Name Class Date Page6 Practice 2-5 Proving Angles Congruent Find the values of the variables. 1. 2. (2x # 10)! (3x # 40)! (6y # 10)! (6y " 10)! 3. 4. 32! (4z # 10)! z! (9x " 4)! 5. 6. (7x " 3)! (4y)! 65! (4x " 1)! (6y)! Write true or false. 7. &1 and &2 are vertical angles. © Pearson Education, Inc. All rights reserved. 8. &2 and &3 are supplementary angles. 9. m&1 = m&3 10. m&3 + m&4 = 180 2 1 3 4 11. m&1 + m&3 = 180 12. &4 and &2 are adjacent angles. Write three conclusions that can be drawn from each figure. 13. 14. 15. O P M B C B D 125! N Q A O E A W C D Geometry Chapter 2 Lesson 2-5 Practice 5 Name Class Date Page7 Practice 3-1 Properties of Parallel Lines Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles. 1. 2. 1 3. 1 2 1 2 2 4. 5. 6. 1 2 1 1 2 2 Use the figure on the right to answer Exercises 7–9. t 7. Name all pairs of corresponding angles formed by the transversal t and lines s and c. 1 2 4 3 8. Name all pairs of alternate interior angles formed by the transversal t and lines s and c. s 5 6 7 8 9. Name all pairs of same-side interior angles formed by the transversal t and lines s and c. c Find ml1 and then ml2. Justify each answer. 10. 11. 12. 135" 2 © Pearson Education, Inc. All rights reserved. 100" 1 1 75" 1 2 2 Algebra Find the value of x. Then find the measure of each angle. 13. x" (x # 26)" 14. 15. x" 2 (7x)" (x ! 55)" (3x # 5)" 16. Developing Proof Supply the missing reasons in this two-column proof. Given: a 6 b Prove: !1 ! !3 Statements Reasons 1. a 6 b 1. Given 2. !1 ! !2 a. 9 b. 9 c. 9 3. !2 ! !3 4. !1 ! !3 Geometry Chapter 3 a 3 2 1 Lesson 3-1 Practice b 1 Name Class Date Page8 Practice 3-2 Proving Lines Parallel 1. Developing Proof Complete the paragraph proof for the figure shown. Given: !RQT and !QTS are supplementary. !TSV and !SVU are supplementary. * ) * ) Prove: QR 6 UV Proof Because !RQT and !QTS are supplementary, !RQT and !QTS are a. 9 angles. By the Same-Side Interior Angles Theorem, b. 9 6 c. 9. Because !TSV and !SVU are supplementary, * ) * !TSV ) and !SVU are d. 9 angles. By the e. 9 Theorem, TS 6 UV . * ) * ) * ) * ) Because QR and UV both are parallel to f. 9, QR 6 UV by Theorem g. 9. Q R T S U V Which lines or segments are parallel? Justify your answer with a theorem or postulate. m ! n 3. v 110" 70" 5. A d o R 30" 6. 70" H 30" T B G F H D a 7. 96° E D U C 84° 101° b 79° c I 100" 55" A A C 125" o 65" 115" B 4. i d Algebra Find the value of x for which a n t. 8. a a 9. t t 10. (3x)" (x # 20)" 93" (x # 44)" a t (x ! 20)" (2x ! 10)" 11. (x ! 30)" a 12. 13. (2x ! 75)" a 80" t 130" 70" t 2 (x ! 20) Lesson 3-2 Practice t a (x # 35)" (2x ! 20)" Geometry Chapter 3 © Pearson Education, Inc. All rights reserved. 2. LOGICREVIEWASGN#18 Writeeachstatementasabiconditional. 1. Congruentanglesareangleswithequalmeasure. 2. Thewholenumbersarethenonnegativeintegers. Page9 NAME___________________________ Writethetwostatementsthatformeachbiconditional. 3. Twolinesareparallelifandonlyiftheyarecoplanaranddonotintersect. Eachconditionalstatementbelowistrue.Writeitsconverse.Iftheconverseisalsotrue,combine thestatementsasabiconditional. 4. Iftwosegmentshavethesamelength,thentheyarecongruent. Writetheconverseofeachconditionalstatement. 5. Ifatriangleisarighttriangle,thenithasa90°angle. 6. Ifyoudonotwork,youdonotgetpaid. Writeeachsentenceasaconditional. 7. Glassobjectsarefragile. 8. Allobtuseangleshavemeasuregreaterthan90. 9. Goodweathermakesapicnicenjoyable. Writetheconverseofeachconditionalstatement.Determinethetruthvaluesoftheoriginal conditionalanditsconverse. 10. IfyoutravelfromtheUnitedStatestoKenya,thenyouhaveapassport. 11. IfyouareinIndiana,thenyouareinIndianapolis. 12. Iftwoangleshavemeasure90,thentheanglesarecongruent. Writethenegationofeachstatement. 13. Twoanglesarecongruent. 14. Theangleisnotobtuse. Write(a)theinverseand(b)thecontrapositiveofeachconditionalstatement. 15. Ifafigureisasquare,thenallofitsanglesarerightangles. 16. Ifafigureisarectangle,thenithasfoursides. Write(a)theinverseand(b)thecontrapositiveofeachstatement.Givethetruthvalueofeach. 17. IfyouliveinSarasota,thenyouliveinFlorida. 18. Iffourpointsarecollinear,thentheyarecoplanar. Writethefirststepofanindirectproof. 19. Itisrainingoutside. 20. Atleastoneangleisobtuse. ForExercises29–32,writeaconvincingargumentthatusesindirectreasoning. 21. Freshskidmarksappearbehindagreencaratthesceneofanaccident.Showthatthedriverofthe greencarappliedthebrakes. 22. Anobtusetrianglecannotcontainarightangle. Page10 UsetheLawofDetachmenttodrawaconclusion. 23. IfthevolleyballteamwinsonTuesdaynight,thenpracticeiscancelledforWednesday. Thevolleyballteamwon3setsto0onTuesdaynight. UsetheLawofSyllogismtodrawaconclusion. 24. Ifyouvacationinthemountains,thenyoumustlikethesnow. Ifyoulikethesnow,thenyouwilllikeColorado. UsetheLawofDetachmentandtheLawofSyllogismtodrawconclusionsfromthefollowing statements. 25. IfyouliveinElPaso,thenyouliveinTexas. IfyouliveinTexas,thenyouliveinthelargeststateintheUnitedStates. NatalialivesinElPaso. 26. Ifitdoesnotrain,thesoftballteamwillhaveagame. Ifthesoftballteamhasagame,theteammemberswillwarmuphittingasoftball. ItdoesnotrainonWednesday. EXTRACREDIT 1. Alan,Ben,andCalareseatedasshownwiththeireyesclosed.Dianeplacesahatoneachoftheir headsfromaboxtheyknowcontains3redand2bluehats.Theyopentheireyesandlook forward.Alansays,“IcannotdeducewhatcolorhatI’mwearing.”Hearingthat,Bensays,“Icannot deducewhatcolorI’mwearing,either.”Calthensays,“IknowwhatcolorI’mwearing!”Howdoes Calknowthecolorofhishat? Page11 Find the sequence rule (function rule) for each. 1. n 1 2 3 4 f(n) -8 -10 -12 -14 2. n 1 2 3 4 f(n) 10 17 24 31 3. n 1 2 3 4 f(n) 3 1 -1 -3 4. n 1 2 3 f(n) 1 2 4 … n … 35 … n … 20 … n … 80 4 5 … n 20 8 16 Page12 Chapter 2 test review Name___________________________ Period_____ Find the missing angles. Show work by writing angles in picture too. Page13 Use the following conditional statement to answer questions 13-18. “If two lines are parallel, then they are coplanar and never intersect.” 13. Write the converse of the conditional statement. 14. Are the conditional and converse true? If true, write them as a biconditional statement. If false, give a counterexample for the false statement. 15. Write the inverse of the conditional statement. 16. Is the inverse true or false? If false, give a counterexample. 17. Write the contrapositive of the conditional statement. 18. Is the contrapositive true or false? If false, give a counterexample. Is each statement a good definition? If not, find a counterexample.