NAME 3-1 DATE PERIOD Study Guide and Intervention Parallel Lines and Transversals Relationships Between Lines and Planes When two n Example P Q โ m S R Refer to the figure at the right to identify each of the following. a. all planes parallel to plane ABD plane EFH b. all segments parallel to ๐ช๐ฎ B ๐ต๐น , ๐ท๐ป, ๐ด๐ธ C F c. all segments skew to ๐ฌ๐ฏ G A D ๐ต๐น, ๐ถ๐บ, ๐ต๐ท, ๐ถ๐ท, and ๐ด๐ต E H Exercises Refer to the figure at the right to identify each of the following. 1. all planes that intersect plane OPT N O 2. all segments parallel to ๐๐ U M 3. all segments that intersect ๐๐ T P R S Refer to the figure at the right to identify each of the following. 4. all segments parallel to ๐๐ 5. all planes that intersect plane MHE N M E H Q 6. all segments parallel to ๐๐ T 7. all segments skew to ๐ด๐บ O X R A S G Chapter 3 5 Glencoe Geometry Lesson 3-1 lines lie in the same plane and do not intersect, they are parallel. Lines that do not intersect and are not coplanar are skew lines. In the figure, โ is parallel to m, or โ โฅ ๐ You can also write ๐๐ โฅ ๐ ๐. Similarly, if two planes do not intersect, they are parallel planes. NAME 3-1 DATE PERIOD Study Guide and Intervention (continued) Parallel Lines and Transversals Angle Relationships A line that intersects two or more other lines at two different points in a plane is called a transversal. In the figure below, line t is a transversal. Two lines and a transversal form eight angles. Some pairs of the angles have special names. The following chart lists the pairs of angles and their names. Angle Pairs Name โ 3, โ 4, โ 5, and โ 6 interior angles โ 3 and โ 5; โ 4 andโ 6 alternate interior angles โ 3 and โ 6; โ 4 and โ 5 consecutive interior angles โ 1, โ 2, โ 7, and โ 8 exterior angles โ 1 and โ 7; โ 2 and โ 8; alternate exterior angles โ 1 and โ 5; โ 2 and โ 6; โ 3 and โ 7; โ 4 and โ 8 corresponding angles t 1 2 4 3 5 6 8 7 Example Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a. โ 10 and โ 16 m n p 1 2 4 3 5 6 8 7 b. โ 4 and โ 12 alternate exterior angles q 9 10 12 11 13 14 16 15 n โ corresponding angles c. โ 12 and โ 13 d. โ 3 and โ 9 consecutive interior angles alternate interior angles Exercises Use the figure in the Example for Exercises 1โ12. Identify the transversal connecting each pair of angles. 1. โ 9 and โ 13 2. โ 5 and โ 14 3. โ 4 and โ 6 Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 4. โ 1 and โ 5 5. โ 6 and โ 14 6. โ 2 and โ 8 7. โ 3 and โ 11 8. โ 12 and โ 3 9. โ 4 and โ 6 10. โ 6 and โ 16 11. โ 11 and โ 14 12. โ 10 and โ 16 Chapter 3 6 Glencoe Geometry