CHAPTER 1 B Organizer 1. Draw and label plane N containing two lines that intersect at B. Objective: Assess students’ 2. four noncoplanar points GI mastery of concepts and skills in Chapter 1. < [email protected]<I 2. Possible answer: D, E, C, A Use the figure to name each of the following. 3. Possible Answer: BE 3. line containing B and E 4. The coordinate of A is -3, and the coordinate of B is 0.5. Find AB. 3.5 5. E, F, and G represent mile markers along a straight highway. Find EF. 14 Online Edition ÈÝÊÊ{ ÎÝ xÝÊÊn − 6. J is the midpoint of HK. Find HJ, JK, and HK. 9; 9; 18 Resources ÎÝÊÊx ÝÊÊÎ Classify each angle by its measure. 7. m∠LMP = 70° acute 9. m∠PMN = 125° obtuse ° ) ( 10. TV bisects ∠RTS. If the m∠RTV = 16x - 6 and m∠VTS = (13x + 9)°, what is the m∠RTV? 74° Assessment Resources Chapter 1 Tests • Free Response (Levels A, B, C) 8. m∠QMN = 90° rt. 11. An angle’s measure is 5 degrees less than 3 times the measure of its supplement. Find the measure of the angle and its supplement. 133.75°; 46.25° • Multiple Choice (Levels A, B, C) Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. • Performance Assessment 12. ∠2 and ∠3 only adj. 13. ∠4 and ∠5 adj. and 14. ∠1 and ∠4 not adj. a lin. pair £ 15. Find the perimeter and area of a rectangle with b = 8 ft and h = 4 ft. P = 24 ft; A = 32 ft Test & Practice Generator Ó Î x { 2 Find the circumference and area of each circle to the nearest tenth. 8.8 cm; 16. 94.2 m; 706.9 m 2 6.2 cm 2 19. Find the midpoint of the segment with endpoints (-4, 6) and (3, 2). (-0.5, 4) 17. 78.5 ft; 490.9 ft 2 16. r = 15 m 17. d = 25 ft 18. d = 2.8 cm − 20. M is the midpoint of LN. M has coordinates (-5, 1), and L has coordinates (2, 4). Find the coordinates of N. (-12, -2) − − 21. Given A(-5, 1), B(-1, 3), C(1, 4), and D (4, 1), is AB CD? Explain. no; AB ≈ 4.5; CD ≈ 4.2 Identify each transformation. Then use arrow notation to describe the transformation. 22. + -Ī 23. 8 ,Ī 180° rotation; QRS → QRS , - A(-2, -2); B(1, 1); C(2, -2) 64 Chapter 1 < 8Ī <Ī 9Ī reflection; WXYZ → WXYZ { Þ y BĪ x Ý { ä { AĪ CĪ Chapter 1 Foundations for Geometry ge07se_c01_0060_0069.indd 64 KEYWORD: MG7 Resources 9 7Ī +Ī 24. A designer used the translation (x, y) → (x + 3, y - 3) to transform a triangular-shaped pin ABC. Find the coordinates and draw the image of ABC. 64 7 12/2/05 4:04:02 PM CHAPTER 2 Organizer Find the next item in each pattern. 2. 405, 135, 45, 15, … 5 1. Objective: Assess students’ GI @<I 3. Complete the conjecture “The sum of two even numbers is ? . ” even −−− 4. Show that the conjecture “All complementary angles are adjacent” is false by finding a counterexample. mastery of concepts and skills in Chapter 2. <D Online Edition 5. Identify the hypothesis and conclusion of the conditional statement “The show is cancelled if it rains.” 6. Write a conditional statement from the sentence “Parallel lines do not intersect.” If 2 lines are , then they do not intersect. Resources Determine if each conditional is true. If false, give a counterexample. Assessment Resources 7. If two lines intersect, then they form four right angles. F Chapter 2 Tests 8. If a number is divisible by 10, then it is divisible by 5. T • Free Response (Levels A, B, C) Use the conditional “If you live in the United States, then you live in Kentucky” for Items 9–11. Write the indicated type of statement and determine its truth value. • Multiple Choice (Levels A, B, C) 9. converse 10. inverse 11. contrapositive 12. Determine if the following conjecture is valid by the Law of Detachment. Given: If it is colder than 50°F, Tom wears a sweater. It is 46°F today. Conjecture: Tom is wearing a sweater. valid • Performance Assessment Test & Practice Generator 13. Use the Law of Syllogism to draw a conclusion from the given information. Given: If a figure is a square, then it is a quadrilateral. If a figure is a quadrilateral, then it is a polygon. Figure ABCD is a square. Figure ABCD is a polygon. 14. Write the conditional statement and converse within the biconditional “Chad will work on Saturday if and only if he gets paid overtime.” −− 15. Determine if the biconditional “B is the midpoint of AC iff AB = BC” is true. If false, give a counterexample. F; B is not between A and C. Solve each equation. Write a justification for each step. 16. 8 - 5s = 1 17. 0.4t + 3 = 1.6 18. 38 = -3w + 2 Identify the property that justifies each statement. 19. If 2x = y and y = 7, then 2x = 7. Trans. Prop. of = 21. ∠X ∠P, and ∠P ∠D. So ∠X ∠D. Trans. Prop. of 20. m∠DEF = m∠DEF Reflex. Prop. of = −− −− −− −− 22. If ST XY, then XY ST. Sym. Prop. of Use the given plan to write a proof in each format. Given: ∠AFB ∠EFD Prove: FB bisects ∠AFC. Plan: Since vertical angles are congruent, ∠EFD ∠BFC. Use the Transitive Property to conclude that ∠AFB ∠BFC. Thus FB bisects ∠AFC by the definition of angle bisector. 23. two-column proof 134 24. paragraph proof 4. Possible answer: ∠1 and ∠2 are comp., but not adj. ge07se_c02_0130_0139.indd 134 7. Possible answer: 134 Chapter 2 25. flowchart proof Chapter 2 Geometric Reasoning Answers KEYWORD: MG7 Resources 9. If you live in Kentucky, then you live in the United States; T. 10. If you do not live in the United States, then you do not live in Kentucky; T. 11. If you do not live in Kentucky, then you do not live in the United States; F. 14. Conditional: If Chad works on Saturday, then he gets paid overtime. Converse: If Chad gets paid overtime, then he will work on Saturday. 16. 8 - 5s = 1 (Given); -5s = -7 (Subtr. Prop. of =); s = 1.4 (Div. Prop. of =) 17. 0.4t + 3 = 1.6 (Given); 0.4t = -1.4 (Subtr. Prop. of =); t = -3.5 (Div. Prop. of =) 18. 38 = -3w + 2 (Given); 36 = -3w (Subtr. Prop. of =); -12 = w (Div. Prop. of =) 23–25. See p. A13. 12/2/05 5:42:40 PM CHAPTER 3 Organizer Identify each of the following. 1. a pair of parallel planes Objective: Assess students’ GI @<I −− −− 2. a pair of parallel segments AC DF mastery of concepts and skills in Chapter 3. <D 3. a pair of skew segments Online Edition Find each angle measure. 4. 5. 6. ÎÝÊÊÓ£®Â {ÓÝÊÊ®Â ÓäÝÊÊ£Ç®Â {ÝÊÊ®Â Resources ÎxÝÊÊ£Ó®Â ÓÈÝÊÊÇ®Â Assessment Resources Chapter 3 Tests Use the given information and the theorems and postulates you have learned to show f g. • Free Response (Levels A, B, C) • Multiple Choice (Levels A, B, C) • Performance Assessment 7. m∠4 = (16x + 20)°, m∠5 = (12x + 32)°, x = 3 £ Î Ó { 8. m∠3 = (18x + 6)°, m∠5 = (21x + 18)°, x = 4 v Write a two-column proof. £ 9. Given: ∠1 ∠2, n ⊥ Test & Practice Generator } « Prove: n ⊥ m x È Ç n Ű Ó _ m= 4 5 Use the slope formula to determine the slope of each line. 10. Þ _ m= 7 2 7 Ó 11. Ý ä { Ó { { m=0 Ó Ó - { Ó < {Ý ä { Þ Ó Ó { Ó 8 12. Þ { Ó / ä Ó { Ý Ó 9 { 32 _ 13. Greg is on a 32-mile bicycle trail from Elroy, Wisconsin, to Sparta, Wisconsin. m = ≈ 7.1; 4.5 He leaves Elroy at 9:30 A.M. and arrives in Sparta at 2:00 P.M. Graph the line Greg’s average speed that represents Greg’s distance from Elroy at a given time. Find and interpret was about 7.1 mi/h. the slope of the line. and ST for Q(3, 3), R(6, -5), S(-4, 6), and T(-1, -2). Use slopes to 14. Graph QR determine whether the lines are parallel, perpendicular, or neither. 3 in point-slope form. y + 5 = - 3 (x + 2) 15. Write the equation of the line through (-2, -5) with slope - _ 4 4 16. Determine whether the lines 6x + y = 3 and 2x + 3y = 1 are parallel, intersect, or coincide. intersect _ 206 Chapter 3 Parallel and Perpendicular Lines Answers 14. 1. plane ABC plane DEF −− −− ge07se_c03_0202_0211.indd 206 3. Possible answer: AB and CF are skew. 4. Both labeled angles measure 57°. S 6. Both labeled angles measure 117°. 8. m∠3 = 78°, and m∠5 = 102°, so m∠3 + m∠5 = 180°. f g by the Conv. of Same-Side Int. Thm. KEYWORD: MG7 Resources 206 Chapter 3 9. 1. ∠1 ∠2, n ⊥ (Given) 2. m (Conv. of Corr. Post.) 3. n ⊥ m (⊥ Transv. Thm.) T 5. Both labeled angles measure 97°. 7. m∠4 = 68°, and m∠5 = 68°, so ∠4 ∠5. f g by the Conv. of Alt. Int. Thm. Q x R 12/2/05 6:02:12 PM CHAPTER 4 Organizer 1. Classify ACD by its angle measures. rt. 2. ACD GI mastery of concepts and skills in Chapter 4. < x°Ç Classify each triangle by its side lengths. Objective: Assess students’ [email protected]<I 3. ABC scalene 4. ABD isosc. Given: XYZ JKL Identify the congruent corresponding parts. −− −− 6. JL ? 7. ∠Y ? XZ ∠K −−−− −−−− −− −− 10. Given: T is the midpoint of PR and SQ. Prove: PTS RTQ Resources Assessment Resources Chapter 4 Tests • Free Response (Levels A, B, C) Î scalene , 5. While surveying the triangular plot of land shown, a surveyor finds that m∠S = 43°. The measure of ∠RTP is twice that of ∠RTS. What is m∠R? 77° Online Edition x {ÎÂ - / 8. ∠L * −− 9. YZ ? ∠Z −−−− −− ? KL −−−− * / - + , • Multiple Choice (Levels A, B, C) 11. The figure represents a walkway with −− triangular supports. Given that GJ bisects ∠HGK and ∠H ∠K, use AAS to prove HGJ KGJ • Performance Assessment Test & Practice Generator −− −− 12. Given: AB DC, −− −− AB ⊥ AC, −− −− DC ⊥ DB Prove: ABC DCB Answers −− −− 10. 1. T is the mdpt. of PR and SQ. (Given) −− −− −− −− 2. PT RT, ST QT (Def. of mdpt.) 3. ∠PTS ∠RTQ (Vert. Thm.) 4. PTS RTQ (SAS Steps 2, 3) −− −− 13. Given: PQ SR, ∠S ∠Q −− −− Prove: PS QR * + - , 14. Position a right triangle with legs 3 m and 4 m long in the coordinate plane. Give the coordinates of each vertex. 15. Assign coordinates to each vertex and write a coordinate proof. Given: Square ABCD −− −− Prove: AC BD Find each value. 16. y 17. m∠S -5 xÊÊ££Þ®Â - * 44° xÈÂ , / + 18. Given: Isosceles ABC has coordinates A(2a, 0), B(0, 2b), and C(-2a, 0). −− −− D is the midpoint of AC, and E is the midpoint of AB. Prove: AED is isosceles. 288 Chapter 4 Triangle Congruence Answers 11. 1. ∠H ∠K (Given) −− 2. GJ bisects ∠HGK. (Given) 3. ∠ HGJ ∠ KGJ (Def. of bisect) −− −− 4. JG JG (Reflex. Prop. of ) 5. HGJ KGJ (AAS Steps 1, 3, 4) −− −− −− −− 12. 1. AB ⊥ AC, DC ⊥ DB (Given) 2. ∠BAC and ∠CDB are rt. . (Def. of ⊥) 3. ABC and DCB are rt. . (Def. of rt. ) −− −− 4. AB DC (Given) −− −− 5. BC CB (Reflex. Prop. of ) 6. ABC DCB (HL Steps 5, 4) ge07se_c04_0284_0293.indd 288 KEYWORD: MG7 Resources 288 Chapter 4 −− −− 13. 1. PQ SR (Given) 2. ∠QPR ∠SRP (Alt. Int. Thm.) 3. ∠S ∠Q (Given) −− −− 4. PR RP (Reflex. Prop. of ) 5. QPR SRP (AAS Steps 2, 3, 4) 6. ∠SPR ∠QRP (CPCTC) −− −− 7. PS QR (Conv. of Alt. Int. Thm.) y m 14. x m 15, 18. See p. A17. 6/10/06 1:38:53 PM CHAPTER 5 Organizer Find each measure. 1. KL 9.8 Objective: Assess students’ GI mastery of concepts and skills in Chapter 5. < [email protected]<I 2. m∠WXY 34° £ä°Ó °n Online Edition £ä°Ó Assessment Resources {° • Free Response (Levels A, B, C) , Ê {°{ Î°Ç / * Ê Ê RS = 6.8; RQ = 4.9 ÓxÂ {ÓÂ 6. In XYZ, XC = 261, and ZW = 118. Find XW, BW, and BZ. m∠GEF = 44°; distance −− from G to DF = 3.7 + ÊxÊ 9 Chapter 5 Tests < −− −− 5. EG and FG are angle bisectors of DEF. Find m∠GEF and the −− distance from G to DF. Î°{ ÊÓÊ Î −−− −−− −− 4. MQ, NQ, and PQ are the perpendicular bisectors of RST. Find RS and RQ. Resources Ê Î £ÇÂ 8 3. BC 21 7 XW = 174; BW = 59; BZ = 177 8 7 9 < 7. Find the orthocenter of JKL with vertices J(-5, 2), K(-5, 10), and L(1, 4). (-3, 4) • Multiple Choice (Levels A, B, C) 8. In GHJ at right, find PR, GJ, and m∠GRP. PR = 51; GJ = 148; m∠GRP = 71° • Performance Assessment 9. Write an indirect proof that two obtuse angles cannot form a linear pair. 10. Write the angles of BEH in order from £°x smallest to largest. Test & Practice Generator ∠E, ∠B, ∠H , ÎÎÂ x£ / xÎÂ {Â −− −− −− TY, RY, RT £°È + Ç£Â 11. Write the sides of , RTY in order from shortest to longest. Ó°{ Ç{ * 9 12. The distance from Arville to Branton is 114 miles. The distance from Branton to Camford is 247 miles. If the three towns form a triangle, what is the range of distances from Arville to Camford? 13. Compare m∠SPV and m∠ZPV. * ÓÓ £ä £{ ÓÓ m∠SPV < m∠ZPV 14. Find the range of values for x. - £x < Ó{Â {Ý£ä®Â 2.5 < x < 8.5 6 Ó£ 15. Find the missing side length in the triangle. Tell if the side lengths form a Pythagorean triple. Explain. Ó{ 16. Tell if the measures 18, 20, and 27 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. triangle; obtuse 17. An IMAX screen is 62 feet tall and 82 feet wide. What is the length of the screen’s diagonal? Round to the nearest inch. 102 ft 10 in. Find the values of the variables. Give your answers in simplest radical form. 18. 2 x = 10 √ Óä {xÂ 19. ÎÓ Ý ÈäÂ x = 16; y = 16 √3 20. Ý Ý 9. Possible answer: Given: ∠1 and ∠2 form a lin. pair. Prove: ∠1 and ∠2 cannot both be obtuse . ge07se_c05_0366_0375.indd 370 370 Chapter 5 3 8 √ _ ; 3 3 16 √ y=_ x= 3 Chapter 5 Properties and Attributes of Triangles Answers KEYWORD: MG7 Resources ÎäÂ Þ Þ 370 n Proof: Assume ∠1 and ∠2 are both obtuse . By the def. of obtuse, m∠1 > 90° and m∠2 > 90°. If the 2 inequalities are added, m∠1 + m∠2 > 180°. However, by the Lin. Pair Thm., ∠1 and ∠2 are supp. By the def. of supp. , this means that m∠1 + m∠2 = 180°. So m∠1 + m∠2 > 180° contradicts the given information. The assumption that ∠1 and ∠2 are both obtuse is false. Therefore ∠1 and ∠2 cannot both be obtuse. 12. greater than 133 mi and less than 361 mi ; the side lengths do not form a 15. 3 √15 Pythagorean triple because 3 √ 15 is not a whole number. 12/2/05 7:48:29 PM

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