Parallel and Perpendicular Lines CHAPTER 3 Parallel and Perpendicular Lines
3.1 IDENTIFY PAIRS OF LINES AND ANGLES
Vocabulary ┴ Types of Lines Symbol Definition / Characteristics Parallel lines Perpendicular Lines Skew lines n/a never intersect are on the same plane have the same slope cross to form 90 angles ┴ are on the same plane never intersect do not lie on the same plane
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? Line(s) parallel to line CD and containing point A Line(s) skew to line CD and containing point A Line(s) perpendicular to line CD and containing point A Plane(s) parallel to plane EFG and containing point A Line BA Line AH Line DA Plane DCB
Postulates 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. .
Perpendicular Postulate There is exactly 1 line through a point perpendicular to another line. .
Identifying Parallel and Perpendicular Lines EXAMPLE 2 Identifying Parallel and Perpendicular Lines The given line markings show how the roads are related to one another. Name a pair of parallel lines. Name a pair of perpendicular lines. Is line FE parallel to line AC ? Explain.
Description/ Properties Angle Pairs - review (formed by the intersection of 2 lines) Description/ Properties Picture Vertical Angles Linear pair angles that are opposite one another Name 2 pairs of vertical angles in the picture above: These ’s are = Hyperlink Name two pairs of vertical angles How are vertical angle related? Name all four adjacent angles How are the adjacent angles related? What is meant by supplementary angles? Name four pairs of supplementary angles What if l2 ┴ l2, what would the measurement be of each of the angles? 1 & 4 2 & 3 Name 4 sets of linear pairs in the picture above: angles that are both adjacent and supplementary (next to) ( __ +___ = 180 ) 1 & 2 2 & 4 3 & 4 3 & 1
Transversal a line that crosses 2 other lines
(formed by a transversal) 5 6 1 2 7 8 Angle Pairs 3 4 (formed by a transversal) Angles are…. Angles are on the ______ side of the transversal Picture Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior Angles in the same position of each intersection same opposite inside of the 2 lines outside of the 2 lines opposite inside the 2 lines and form a linear pair same
Example 3 Identify all pairs of angles of the given type: Extra Practice Example 3 Identify all pairs of angles of the given type: Corresponding E. Vertical Angles Alternate interior Alternate exterior F. Linear Pairs Consecutive interior 1 & 5 2 & 6 3 & 7 4 & 8 A & E B & F D & H C & G 1 & 4 2 & 3 5 & 8 6 & 7 4 & 5 2 & 7 D & E B & G 1 & 8 3 & 6 A & H C & F 1 & 2 2 & 4 3 & 4 3 & 1 5 & 6 5 & 7 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 Alternate Interior angles Corresponding angles