Parallel Lines and Transversals Geometry D – Section 3.1

Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel Arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines. AB || CD

Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. AB || CD

Parallel Lines and Transversals Plane – A plane is a flat surface with no thickness (2D) -Top of a sheet of paper that extends forever Coplanar – A set of points, lines, line segments, rays or any other geometrical shapes that lie on the same plane are said to be Coplanar.

Parallel Lines and Transversals Skew Lines – Two lines are skew if they are not in the same plane (not coplanar) AND do not intersect. AB does not intersect CD . Since the lines are not in the same plane, they are skew lines.

Parallel Lines and Transversals For the rectangular box shown below, find All planes parallel to plane CDEF.

Parallel Lines and Transversals For the rectangular box shown below, find All planes parallel to plane CDEF. Plane BAHG (or any plane with BAHG).

Parallel Lines and Transversals For the rectangular box shown below, find The intersection of plane AHED and plane CFED.

Parallel Lines and Transversals For the rectangular box shown below, find The intersection of plane AHED and plane CFED.

Parallel Lines and Transversals For the rectangular box shown below, find All segments parallel to CD.

Parallel Lines and Transversals For the rectangular box shown below, find All segments parallel to CD. AB, GH, EF

Parallel Lines and Transversals For the rectangular box shown below, find All segments that intersect CF.

Parallel Lines and Transversals For the rectangular box shown below, find All segments that intersect CF.

Parallel Lines and Transversals For the rectangular box shown below, find All lines skew to GF.

Parallel Lines and Transversals For the rectangular box shown below, find All lines skew to GF. Segments HE, AD, and BC are || or in the same plane. Segments GH, EF, BG and CF intersect and are in the same plane. These segments are not skew to GF.

Parallel Lines and Transversals A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. A transversal is said to “cut” the lines. Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.

Parallel Lines and Transversals Identifying Angles - Exterior Angles are on the exterior (outside) of the two lines cut by the transversal. 1 3 5 7 2 4 6 8 The exterior angles are:

Parallel Lines and Transversals Identifying Angles - Interior Angles are on the interior (inside) of the two lines cut by the transversal. 1 3 5 7 2 4 6 8 The interior angles are:

Parallel Lines and Transversals Identifying Angles - Consecutive Interior Angles are on the interior of the two lines and on the same side of the transversal. 1 3 5 7 2 4 6 8 Consecutive interior angles are:

Parallel Lines and Transversals Identifying Angles - Alternate Interior Angles are on the interior of the two lines and on opposite sides of the transversal. 1 3 5 7 2 4 6 8 Alternate interior angles are:

Parallel Lines and Transversals Identifying Angles - Alternate Exterior Angles are on the exterior of the two lines and on opposite sides of the transversal. 1 3 5 7 2 4 6 8 Alternate exterior angles are:

Parallel Lines and Transversals Identifying Angles - Corresponding Angles are on the corresponding side of the two lines and on the same side of the transversal. 1 3 5 7 2 4 6 8 Corresponding angles are:

Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 1. Line r is a transversal of lines p and q. True – Line r intersects both lines in a plane. 4 3 2 1 5 6 8 7 2. 2 and 10 are alternate interior angles. 9 10 11 12 False - The angles are corresponding angles on transversal p. 16 15 14 13

Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 3. 3 and 5 are alternate interior angles. False – The angles are vertical angles created by the intersection of q and r. 4 3 2 1 5 6 8 7 4. 1 and 15 are alternate exterior angles. 9 10 11 12 15 16 14 13 True - The angles are alternate exterior angles on transversal p.

Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 5. 6 and 12 are alternate interior angles. True – The angles are alternate interior angles on transversal q. 4 3 2 1 5 6 8 7 6. 10 and 11 are consecutive interior angles. 9 10 11 12 15 16 14 13 True – The angles are consecutive interior angles on transversal s.

Parallel Lines and Transversals Identifying Angles – Check for Understanding Determine if the statement is true or false. If false, correct the statement. 7. 3 and 4 are alternate exterior angles. False – The angles are a linear pair with linear rays on line r. 4 3 2 1 5 6 8 7 8. 16 and 14 are corresponding angles. 9 10 11 12 16 15 14 13 True – The angles are corresponding on transversal s.