CHAPTER 3 Parallel and Perpendicular Lines 3 1

CHAPTER 3 Parallel and Perpendicular Lines

3. 1 IDENTIFY PAIRS OF LINES AND ANGLES

Vocabulary Types of Lines Definition / Characteristics Symbol Parallel lines • never intersect • are on the same plane • have the same slope Perpendicular Lines • cross to form 90 angles • are on the same plane ┴ Skew lines • never intersect • do not lie on the same plane n/a

EXAMPLE 1 Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? 1) 2) 3) 4) Line(s) parallel to line CD and containing point A Line BA Line(s) skew to line CD and containing point A Line AH Line(s) perpendicular to line CD and containing point A Line DA Plane(s) parallel to plane EFG and containing point A Plane DCB

Postulates l A postulate is a true statement, which does not require to be proved.

Parallel Postulate There is exactly 1 line through a point parallel to another line. l.

Perpendicular Postulate There is exactly 1 line through a point perpendicular to another line. l .

EXAMPLE 2 Identifying Parallel and Perpendicular Lines The given line markings show the roads are related to one another. 1. Name a pair of parallel lines. 2. Name a pair of perpendicular lines. 3. Is line FE parallel to line AC ? Explain.

Angle Pairs - review (formed by the intersection of 2 lines) Description/ Properties Vertical Angles angles that are opposite one another l • These ’s are = Linear pair angles that are both adjacent and supplementary (next to) ( __ +___ = 180 ) l Picture Name 2 pairs of vertical angles in the picture above: 1 & 4 2 & 3 Name 4 sets of linear pairs in the picture above: 1 & 2 2 & 4 3 & 1

Transversal a line that crosses 2 other lines

1 2 5 6 3 4 7 8 Angle Pairs (formed by a transversal) Angles are…. Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior Angles are on the ______ side of the transversal in the same position of each intersection same inside of the 2 lines opposite outside of the 2 lines opposite inside the 2 lines and form a linear pair same Picture

Extra Practice Example 3 Identify all pairs of angles of the given type: A. Corresponding E. Vertical Angles 1 & 5 2 & 6 3 & 7 4 & 8 1 & 4 2 & 3 A & E B & F D & H C & G 5 & 8 6 & 7 B. Alternate interior 4 & 5 2 & 7 D & E B & G C. Alternate exterior F. Linear Pairs 1 & 8 3 & 6 1 & 2 2 & 4 3 & 4 A & H C & F 3 & 1 5 & 6 5 & 7 D. Consecutive interior 7 & 8 8 & 6 2 & 5 4 & 7 B & E D & G

GUIDED PRACTICE Classify the pair of numbered angles in each picture Alternate Exterior angles Corresponding angles Alternate Interior angles