PARALLEL AND PERPENDICULAR LINES
Glossary 5
Parallel
Definition of Parallel Lines:
Lines in the same plane that do not intersect.
Perpendicular
Definition of Perpendicular Lines:
Lines that intersect at 90° angles.
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Definition of Right Angle: An angle is a right angle if and
only if its measure is 90°
Right Angle Congruence Theorem:
All right angles are congruent
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.
Parallel Lines with a Transversal Angle Pair Theorems:
Definition of Complementary Angles
Two angles whose measures have a sum of 90°
Corresponding Angles are congruent
Alternate Interior Angles are congruent
Alternate Exterior Angles are congruent
Same-Side Interior are supplementary
Congruent Complements Theorem:
If two angles are complementary to the same angle
(or to congruent angles)
then the two angles are congruent.
Congruent Supplements Theorem:
If two angles are supplementary to the same angle
(or to congruent angles)
then the two angles are congruent.
Slopes of Parallel Lines Postulate: In a coordinate plane,
two non-vertical lines are parallel if and only if they have the
same slope. Any two vertical lines are parallel.
Slopes of Perpendicular Lines Postulate: In a coordinate
plane, two non-vertical lines are perpendicular if and only if
product of their slopes is -1. Vertical and horizontal lines are
perpendicular
3.1 Equal Measure Linear Pair Theorem:
(a.k.a. Perpendicular Linear Pair Theorem)
If two intersecting lines form a linear pair of angles with
equal measures, then the lines are perpendicular
3.11 Parallel Parallels
If two lines are parallel to the same line, then they are parallel
to each other
Perpendicular Transversal:
If a transversal is perpendicular to one of two perpendicular
lines, then it is perpendicular to the other
3.12 Perpendicular Parallels
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other
Definition SKEW Lines: In 3 dimensional geometry, two lines
that do not intersect and are NOT parallel
3.2 Perpendicular Complementary Theorem
If two sides of two adjacent acute angles are perpendicular,
then the angles complementary.
3.3 Perpendicular 4 Right Angles Theorem
If two lines are perpendicular, then they intersect to form
four right angles.