Chapter 3: 3-1: Parallel Lines and Transversals Geometry Chapter 3: 3-1: Parallel Lines and Transversals
Do Now: Quick Ponder: Review: What are parallel lines? How can we tell if two lines are parallel? Review: If you are tired in class, then you may fall asleep What is the inverse of this statement? What is the converse of this statement?
Definitions: Parallel Lines: are coplanar lines that do not intersect. Notation: Picture: Arrows are used to indicate that lines are parallel.
Definitions (continued) Skew Lines: Are lines that do not intersect and are not coplanar. No Notation Picture:
Definitions (Continued) Parallel Planes: are planes that do not intersect. Notation: None Picture:
Example 1: Identify each of the following using the wedge of cheese below. a) All segments parallel to JP b) A segment skew to KL c) A plane parallel to plane PQR
Example 1: Answers Identify each of the following using the wedge of cheese below. a) All segments parallel to JP - KQ and LR b) A segment skew to KL - JP, PQ, PR c) A plane parallel to plane PQR - Plane JKL
Example 2: In the figure, assume that the lines and planes that appear to be parallel are parallel. Which segments are parallel to AB? Which segments are skew to CD? What are two pairs of parallel planes? What are two segments parallel to plane BCGF?
Example 2: Answers In the figure, assume that the lines and planes that appear to be parallel are parallel. Which segments are parallel to AB? - CD, EF Which segments are skew to CD? - BF, AE, EF, EH, FG What are two pairs of parallel planes? - Plane ABCD is parallel to Plane EFGH - Plane ADHE is parallel to EFGC What are two segments parallel to plane BCGF? AE and HD
Definition: Transversal: A line that intersects two or more coplanar lines at two different points. Notation: None Picture: t is a transversal of lines l and m
Definitions: Interior Angles: Angles that lie in the region between two lines. Here interior angles are:
Definitions: Interior Angles: Angles that lie in the region between two lines. Here interior angles are: <3, <4, <5, <6
Definitions: Exterior Angles: Angles that lie in the region outside of two lines. Here exterior angles are:
Definitions: Exterior Angles: Angles that lie in the region outside of two lines. Here exterior angles are: <1, <2, <7, <8
Definitions: Consecutive Interior Angles: Interior Angles that lie on the same side of a transversal. Here consecutive interior angles are:
Definitions: Consecutive Interior Angles: Interior Angles that lie on the same side of a transversal. Here consecutive interior angles are: <3 and <6 <4 and <5
Definitions: Alternate Interior Angles: are nonadjacent interior angles that lie on opposite sides of a transversal. Alternate Interior Angles:
Definitions: Alternate Interior Angles: are nonadjacent interior angles that lie on opposite sides of a transversal. Alternate Interior Angles: <4 and <6 <5 and <3
Definitions: Alternate Exterior Angles: are nonadjacent exterior angles that lie on opposite sides of a transversal. Alternate Exterior Angles:
Definitions: Alternate Exterior Angles: are nonadjacent exterior angles that lie on opposite sides of a transversal. Alternate Exterior Angles: <1 and <7 <2 and <8
Definitions: Corresponding Angles: lie on the same side of a transversal and on the same side of the two lines the transversal intersects. Corresponding angles:
Definitions: Corresponding Angles: lie on the same side of a transversal and on the same side of the two lines the transversal intersects. Corresponding angles: <1 and <5 <4 and <8 <2 and <6 <3 and <7
Example 3:
Example 4:
Practice Problems Try some on your own/in table groups. As always if you are confused please don’t hesitate to ask me questions.
Exit Ticket Name an example of each: Corresponding Angles Alternate Exterior Angles Consecutive Interior Angles Alternate Interior Angles