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PARALLEL LINES AND
TRANSVERSALS
SECTIONS 3.3-3.4
CORRESPONDING ANGLES POSTULATE
• Two lines cut by a transversal are parallel if and only
if the pairs of corresponding angles are congruent.
ALTERNATE INTERIOR ANGLES
THEOREM
• Two lines cut by a transversal are parallel if and only
if the pairs of alternate interior angles are
congruent.
ALTERNATE EXTERIOR ANGLES
THEOREM
• Two lines but by a transversal are parallel if and only
if the pairs of alternate exterior angles are
congruent.
CONSECUTIVE INTERIOR ANGLES
THEOREM
• Two lines cut by a transversal are parallel if and only
if the pairs of consecutive interior angles are
supplementary.
TRANSITIVE PROPERTY OF PARALLEL
LINES
• If two lines are parallel to the same line, then they
are parallel to each other.
EXAMPLE
• Find each numbered angle.
EXAMPLE
• Find the value of x.
EXAMPLE
• Find the value of x. The picture may not be drawn
to scale.
(3x + 5)o
(7x – 15)o
LINEAR PAIR PERPENDICULAR
THEOREM
• If two lines intersect to form a linear pair of
congruent angles, then the lines are perpendicular.
PERPENDICULAR TRANSVERSAL
THEOREM
• If a transversal is perpendicular to one of two
parallel lines, then it is perpendicular to the other.
LINES PERPENDICULAR TO A
TRANSVERSAL THEOREM
• In a plane, if two lines are perpendicular to the
same line, then they are parallel to each other.
ASSIGNMENT
• p. 142: 3-8, 13-18, 21-24
• p. 153: 17-23