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Theorems, Postulates, Definitions and Properties
3.2
Postulate - If two parallel lines are cut by a transversal, then corresponding angles
are congruent.
Theorem - If two parallel lines are cut by a transversal then each pair of alternate
interior angles are congruent.
Theorem - If two parallel lines are cut by a transversal then each pair of alternate
exterior angles are congruent.
Theorem - If two parallel lines are cut by a transversal then each pair of interior
angles on the same side of the transversal are supplementary.
Theorem - If two parallel lines are cut by a transversal then each pair of exterior
angles on the same side of the transversal are supplementary.
3.3
Postulate - If two lines and a transversal form corresponding angles that are
congruent, then the lines are parallel.
Theorem - If two lines are cut by a transversal so a pair of alternate interior angles
are congruent then the lines are parallel.
Theorem - If two lines are cut by a transversal so a pair of alternate exterior angles
are congruent then the lines are parallel.
Theorem - If two lines are cut by a transversal so a pair of interior angles on the
same side of the transversal are supplementary then the lines are parallel.
Theorem - If two lines are cut by a transversal so a pair of exterior angles on the
same side of the transversal are supplementary then the lines are parallel.
3.4
Theorem - If two lines are parallel to the same line, then they are parallel to each
other.
Theorem – In a plane, if two lines are perpendicular to the same line, then they are
parallel to each other.
Theorem - In a plane, if a line is perpendicular to one of two parallel lines, then it
is also perpendicular to the other.
3.5
Postulate - Parallel Postulate – Through a point not on a line, there is one and only
line parallel to the given line.
Theorem - The sum of the measures of the interior angles of a triangle is 180
degrees.
Theorem - The measure of each exterior angle of a triangle is equal to the sum of
the measures of its two remote interior angles.
3.6
Postulate - Perpendicular Postulate – Through a point not a line, there is one and
only line perpendicular to the given line.