Answers (Lesson 3-1)

1 Glencoe/McGraw-HillA2 Glencoe GeometryStudy guide and InterventionParallel Lines and TransversalsNAME _____ DATE _____ PERIOD _____3-13-1 Glencoe/McGraw-Hill125 Glencoe GeometryLesson 3-1 Relationships Between Lines and PlanesWhen two lines lie in the same plane and do not intersect, they are that do not intersect and are not coplanar are skew the figure, is parallel to m,or || can also write PQ ||RS .Similarly, if two planes do not intersect, they are parallel Name all planes that are parallel to plane EFHb. Name all segments that are parallel to C G .B F ,D H ,and A E c. Name all segments that are skew to E H .B F ,C G ,B D ,C D ,and A B For Exercises 1 3, refer to the figure at the all planes that intersect plane ,MPS,NOT, all segments that are parallel to N U .O T ,P S ,M R all segments that intersect M P .M R ,M N ,M S ,P S ,P O For Exercises 4 7, refer to the figure at the all segments parallel to Q X .R A ,S G ,T O ,M H ,N E all planes that intersect plane ,NEX,HEX,MNQ,SGO, all segments parallel to Q R.

2 A X ,H O ,M T all segments skew to A G .S T ,T M ,N Q ,Q R ,T O ,M H ,N E ,Q X TSGAXENMHOQRMNOPRUTSABCDEFGHPQRSnm ExampleExampleExercisesExercises Glencoe/McGraw-Hill126 Glencoe GeometryAngle RelationshipsA line that intersects two or more other lines in a plane is calleda the figure below,tis a transversal. Two lines and a transversal form eightangles. Some pairs of the angles have special names. The following chart lists the pairs ofangles and their PairsName 3, 4, 5, and 6interior angles 3 and 5; 4 and 6alternate interior angles 3 and 6; 4 and 5consecutive interior angles 1, 2, 7, and 8exterior angles 1 and 7; 2 and 8alternate exterior angles 1 and 5; 2 and 6; 3 and 7; 4 and 8corresponding anglesIdentify each pair of angles as alternate interior,alternate exterior,corresponding,or 10 and 16b. 4 and 12alternate exterior anglescorresponding anglesc. 12 and 13d. 3 and 9consecutive interior anglesalternate interior anglesUse the figure in the Example for Exercises 1 the transversal that forms each pair of 9 and 13 q2.

3 5 and 14 3. 4 and 6 pIdentify each pair of angles as alternate interior,alternate exterior,corresponding,or consecutive 1 and 55. 6 and 146. 2 and 8correspondingcorrespondingalt. exterior7. 3 and 118. 12 and 39. 4 and 6correspondingconsecutive interioralt. interior10. 6 and 1611. 11 and 1412. 10 and 16alt. interiorconsecutive interioralt. exterior pqn12910111234141365151678tnm12345678 study guide and Intervention (continued)Parallel Lines and TransversalsNAME _____ DATE _____ PERIOD _____3-13-1 ExampleExampleExercisesExercisesAnswers( lesson 3-1) Glencoe/McGraw-HillA6 Glencoe GeometrySkills PracticeAngles and Parallel LinesNAME _____ DATE _____ PERIOD _____3-23-2 Glencoe/McGraw-Hill133 Glencoe GeometryLesson 3-2In the figure,m 2 70. Find the measure of each 3702. 51103. 81104. 11105. 41106. 670In the figure,m 7 100. Find the measure of each 91008. 6809. 88010. 28011. 510012. 11100In the figure,m 3 75 and m 10 115. Find the measure of each 210514.

4 510515. 710516. 1511517. 146518. 965 Find xand yin each 28,y 10,y 15 Find m 1 in each 32 160 120 7x (8x 10) (6y 20) 5x 40 (3y 1) xwzy12436589101112131415167smut124365891 011127qrs12436587 Glencoe/McGraw-Hill134 Glencoe GeometryIn the figure,m 2 92 and m 12 74. Find the measure of each 10922. 8923. 9884. 51065. 111066. 13106 Find xand yin each 14,y 37x 28,y 23 Find m 1 in each a paragraph proof of Theorem : ||m,m||nProve: 1 12 Sample proof:It is given that ||m,so 1 8 by the AlternateExterior Angles Theorem. Since it is given that m||n, 8 12 by the Corresponding Angles , 1 12, since congruence of angles is diagonal brace strengthens the wire fence and prevents it from sagging. The brace makes a 50 angle with the wire as y mn12346578 k91011 12144 62 1100 50 13y (2x 13) (5y 4) 3x (9x 12) (4y 10) nmrs12436589101112131415167 Practice (Average)Angles and Parallel LinesNAME _____ DATE _____ PERIOD _____3-23-2 Answers (Lesson 3-2) Glencoe/McGraw-HillA5 Glencoe GeometryAnswersStudy guide and InterventionAngles and Parallel LinesNAME _____ DATE _____ PERIOD _____3-23-2 Glencoe/McGraw-Hill131 Glencoe GeometryLesson 3-2 Parallel Lines and Angle PairsWhen two parallel lines are cut by a transversal,the following pairs of angles are congruent.

5 Corresponding angles alternate interior angles alternate exterior anglesAlso, consecutive interior angles are the figure,m 2 75. Find the measures of the remaining 1 105 1 and 2 form a linear 3 105 3 and 2 form a linear 4 75 4 and 2 are vertical 5 105 5 and 3 are alternate interior 6 75 6 and 2 are corresponding 7 105 7 and 3 are corresponding 8 75 8 and 6 are vertical the figure,m 3 102. Find the measure of each 51022. 6783. 11 1024. 71025. 151026. 1478In the figure,m 9 80 and m 5 68. Find the measure of each 121008. 1809. 410010. 38011. 76812. 16112wvpq12346578910111214131516pqmn1234 6578910111214131516pmn12346578 ExampleExampleExercisesExercises Glencoe/McGraw-Hill132 Glencoe GeometryAlgebra and Angle MeasuresAlgebra can be used to find unknown values in angles formed by a transversal and parallel m 1 3x 15,m 2 4x 5,m 3 5y,and m 4 6z 3, find xand ||q,so m 1 m 2 because they are corresponding 15 4x 53x 15 3x 4x 5 3x15 x 515 5 x 5 520 xpqrs1234 study guide and Intervention (continued)Angles and Parallel LinesNAME _____ DATE _____ PERIOD _____3-23-2 ExampleExampler||s,so m 2 m 3 because they are corresponding 2 m 375 5y 755 55y 15 yExercisesExercisesFind xand yin each 15;y 19x 6;y 11;y 10x 10;y 25 Find x,y,and zin each 74;y 37;z 25x 30;y 15.

6 Z 1502x 2y 90 x z 2y 106 x (4z 6) (5x 20) 3x 2y 4y (11x 4) (13y 5) (5y 5) 5x (15x 30) (3y 18) 10x 90 (5x 5) (6y 4) (4x 10) Answers (Lesson 3-2) Glencoe/McGraw-HillA9 Glencoe GeometryAnswersSkills PracticeSlopes of LinesNAME _____ DATE _____ PERIOD _____3-33-3 Glencoe/McGraw-Hill139 Glencoe GeometryLesson 3-3 Determine the slope of the line that contains the given ( 1, 2),W(0, 4) ( 2, 5),H(1, 7) (0, 1),D(3, 3) 23 ( 5, 2),K(5, 4) 15 Find the slope of each 34 line parallel to TW line perpendicular to NP 2 43 Determine whether AB and MN are parallel,perpendicular,or (0, 3),B(5, 7),M( 6, 7),N( 2, 1) ( 1, 4),B(2, 5),M( 3, 2),N(3, 0) ( 2, 7),B(4, 2),M( 2, 0),N(2, 6) ( 4, 8),B(4, 6),M( 3, 5),N( 1, 3)parallelperpendicularGraph the line that satisfies each 3, contains A(0, 1) 32 ,contains R( 4, 5) Y(3, 0), parallel to DJ T(0, 2), perpendicular to CX with D( 3, 1) and J(3, 3)with C(0, 3) and X(2, 1)T(0, 2)C(0, 3)X(2, 1)xyOD( 3, 1)J(3, 3)Y(3, 0)xyOR( 4, 5)xyOA(0, 1)xyOxyONTWP Glencoe/McGraw-Hill140 Glencoe GeometryDetermine the slope of the line that contains the given ( 4, 4),R(0, 2) 12 ( 2, 9),P(2, 4) 143 Find the slope of each 23 25 line parallel to GR line perpendicular to PS 25 12 Determine whether KM and ST are parallel,perpendicular,or ( 1, 8),M(1, 6),S( 2, 6),T(2, 10) ( 5, 2),M(5, 4),S( 3, 6),T(3, 4) ( 4, 10),M(2, 8),S(1, 2),T(4, 7) ( 3, 7),M(3, 3),S(0, 4),T(6, 5)parallelperpendicularGraph the line that satisfies each 12 ,contains U(2, 2) 43 ,contains P( 3, 3) B( 4, 2), parallel to FG Z( 3, 0), perpendicular to EK with F(0, 3) and G(4, 2)with E( 2, 4) and K(2, 2) Take Two began renting DVDs at their video store, business 2000 and 2003, profits increased at an average rate of $12,000 per year.

7 Totalprofits in 2003 were $46,000. If profits continue to increase at the same rate, what willthe total profit be in 2009?$118,000K(2, 2)E( 2, 4)Z( 3, 0)xyOF(0, 3)B( 4, 2)G(4, 2)xyOP( 3, 3)xyOU(2, 2)xyOxyORGSPMLP ractice (Average)Slopes of LinesNAME _____ DATE _____ PERIOD _____3-33-3 Answers (Lesson 3-3) Glencoe/McGraw-HillA11 Glencoe GeometryAnswersStudy guide and InterventionEquations of LinesNAME _____ DATE _____ PERIOD _____3-43-4 Glencoe/McGraw-Hill143 Glencoe GeometryLesson 3-4 Write Equations of LinesYou can write an equation of a line if you are given any ofthe following: the slope and the y-intercept, the slope and the coordinates of a point on the line, or the coordinates of two points on the mis the slope of a line,bis its y-intercept, and (x1,y1) is a point on the line, then: the slope-intercept formof the equation is y mx b, the point-slope formof the equation is y y1 m(x x1).Write an equation inslope-intercept form of the line withslope 2 and y-intercept mx bSlope-intercept formy 2x 4m 2, b 4 The slope-intercept form of the equation ofthe line is y 2x an equation inpoint-slope form of the line with slope 34 that contains (8, 1).

8 Y y1 m(x x1)Point-slope formy 1 34 (x 8)m 34 , (x1, y1) (8, 1)The point-slope form of the equation of theline is y 1 34 (x 8).Example1 Example1 Example2 Example2 ExercisesExercisesWrite an equation in slope-intercept form of the line having the given slope and :2,y-intercept: : 12 ,y-intercept: 4y 2x 3y 12 x : 14 ,y-intercept: :0,y-intercept: 2y 14 x 5y : 53 ,y-intercept: 13 : 3,y-intercept: 8y 53 x 13 y 3x 8 Write an equation in point-slope form of the line having the given slope thatcontains the given 12 ,(3, 1) 2, (4, 2)y 1 12 (x 3)y 2 2(x 4) 1, ( 1, 3) 14 ,( 3, 2)y 3 (x 1)y 2 14 (x 3) 52 ,(0, 3) 0, ( 2, 5)y 3 52 xy 5 0 Glencoe/McGraw-Hill144 Glencoe GeometryWrite Equations to Solve ProblemsMany real-world situations can be modeledusing linear offers computer services to small companies in her city. Shecharges $55 per month for maintaining a web site and $45 per hour for eachservice guide and Intervention (continued)Equations of LinesNAME _____ DATE _____ PERIOD _____3-43-4 ExampleExamplea.

9 Write an equation torepresent the totalmonthly cost Cformaintaining a web siteand for hhours ofservice each hour, the costincreases $45. So the rate ofchange, or slope, is 45. They-intercept is located wherethere are 0 hours, or $ mh b 45h 55b. Donna may change her costs to represent themby the equation C 25h 125, where $125 is thefixed monthly fee for a web site and the cost perhour is $25. Compare her new plan to the old one if a company has 5 12 hours of service calls. Under which plan would Donna earn more?First planFor 5 12 hours of service Donna would earnC 45h 55 45 5 12 55 55 or $ PlanFor 5 12 hours of service Donna would earnC 25h 125 25( ) 125 125 or $ would earn more with the first Exercises 1 4, use the following s current satellite television service charges a flat rate of $ per month for the basicchannels and an additional $10 per month for each premium channel. A competing satellitetelevision service charges a flat rate of $ per month for the basic channels and anadditional $8 per month for each premium an equation in slope-intercept formthat models the total monthly cost foreach satellite service, where pis thenumber of premium service:C 10p service:C 8p third satellite company charges a flatrate of $69 for all channels, including thepremium channels.

10 If Jerri wants to adda fourth premium channel, which servicewould be least expensive?the third Jerri wants to include three premiumchannels in her package, which servicewould be less, her current service or thecompeting service?competing a description of how the fee for thenumber of premium channels is reflectedin the fee for thenumber of premium channelsrepresents the rate of change,or slope, of the ( lesson 3-4) Glencoe/McGraw-HillA15 Glencoe GeometryAnswersSkills PracticeProving Lines ParallelNAME _____ DATE _____ PERIOD _____3-53-5 Glencoe/McGraw-Hill151 Glencoe GeometryLesson 3-5 Given the following information, determine which lines,if any, are parallel. State the postulate or theorem that justifies your 3 72. 9 11a||b; a||b;corr. 3. 2 5 m 12 180 ||m; ||m;cons. int. Find xso that || a reason for each statement in the proof of Theorem : 1 and 2 are C C D Prove:B A ||C D C C D ABC m 1 m Addition Postulate3. 1 and 2 are 1 m 2 of complementary ABC Property of A B C of A ||C D 2 lines are to the same line, thenlines are ||.