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Glencoe Geometry Chapter 3

Postulates and theorems relating to parallel lines and transversals -- directly from the text. Great for practicing complete and accurate wording so you will use them properly in future proofs.
-- Theorem numbers are provided only for reference to the textbook. The important parts to study are the words of the theorems themselves, along with their meanings.

AB
Postulate 3-1 Corresponding AnglesIf two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
Theorem 3-1 Alternate InteriorIf two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent,
Theorem 3-2 Consecutive Interior AnglesIf two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary
Theorem 3-3 Alternate Exterior AngleIf two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent,
Theorem 3-4 Perpendicular TransversalIn a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Postulate 3-5 Parallel PostulateIf there is a line and a point not on the line, then there exists exactly one line though the point that is parallel to the given line.
Postulate 3-4 Corresponding Angles (converse)If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Theorem 3-5 Alt Ext Angles (converse)If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel.
Theorem 3-6 Consecutive Angles (converse)If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.
Theorem 3-8 Perpendicular Lines (converse)In a plane, if two lines are perpendicular to the same line, then they are parallel.
Theorem 3-7 Alt Int Angles (converse)If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel.
Postulate 3-2 Parallel PostulateTwo nonvertical lines have the same slope if and only if they are parallel.
Postulate 3-3 Perpendicular PostulateTwo nonvertical lines are perpendicular if and only if the product of their slopes is -1.
Theprem 2-1 Segment CongruenceCongruence of segments is reflexive, symmetric, and transitive
Theorem 2-2 LP Supplement TheoremIf 2 angles for a linear pair, then they are supplementary angles.
Theorem 2-3 Angle CongruenceCongruence of angles is reflexive, symmetric, and transitive.
Theorem 2-4 Supplementary AnglesAngles supplementary to the same angle or to congruent angles are congruent.
Theorem 2-5 Complementary AnglesAngles complementary to the same angle or to congruent angles are congruent.


Mr Fowler

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