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.

2 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 .A X ,H O ,M T all segments skew to A G.

3 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 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. 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.

5 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.

6 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. 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.

7 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.

8 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.

9 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)

10 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;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)