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DEFINITIONS
Two lines are parallel lines if they do not intersect and are coplanar. In other words ,
parallel lines do not intersect and run in the same direction.
Two lines are skew lines if they do not intersect and are not coplanar. In other words,
skew lines do not intersect but don’t run in the same direction.
Two planes that do not intersect are called parallel planes.
DEFINITIONS
Perpendicular lines are lines that intersect to form a right angle.
Perpendicular planes are planes that intersect to form a right angle.
POSTULATES
Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through
the point parallel to the given line.
Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through
the point perpendicular to the given line.
ANGLES
A transversal is a line that intersects two or more coplanar lines at different points.
Two angles are corresponding angles if they have corresponding positions.
ANGLES
Two angles are alternate interior angles if they lie between the two lines and on
opposite sides of the transversal.
Two angles are alternate exterior angles if they lie outside the two lines and on
opposite sides of the transversal.
Two angles are consecutive interior angles if they lie between the two lines and on the
same side of the transversal.
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.
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
ASSIGNMENT
p. 129: 3-8, 11-18
p. 135: 3-12