Postulates and also theorems relating to parallel lines and also transversals -- straight 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 come study space the words of the theorems themselves, together with their meanings.

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Postulate 3-1 matching Angles
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If 2 parallel lines are cut by a transversal, then each pair of matching angles is congruent.
Theorem 3-1 alternating InteriorIf two parallel lines are cut by a transversal, then each pair of alternating interior angle is congruent,
Theorem 3-2 Consecutive internal AnglesIf 2 parallel lines are reduced by a transversal, then each pair the consecutive interior angles is supplementary
Theorem 3-3 alternative Exterior AngleIf 2 parallel currently are cut by a transversal, climate each pair of alternative exterior angle is congruent,
Theorem 3-4 Perpendicular TransversalIn a plane, if a heat is perpendicular to one of two parallel lines, then it is perpendicular come the other.
Postulate 3-5 Parallel PostulateIf over there is a line and a allude not ~ above the line, climate there exists precisely one heat though the suggest that is parallel to the given line.
Postulate 3-4 matching Angles (converse)If two lines in a aircraft are reduced by a transversal therefore that corresponding angles space congruent, then the lines space parallel.
Theorem 3-5 Alt Ext angles (converse)If 2 lines in a airplane are reduced by a transversal so the a pair of alternating exterior angles is congruent, climate the two lines room parallel.
Theorem 3-6 Consecutive angle (converse)If two lines in a aircraft are reduced by a transversal so the a pair of consecutive interior angles is supplementary, then the lines space parallel.
Theorem 3-8 Perpendicular present (converse)In a plane, if two lines space perpendicular come the very same line, climate they space parallel.
Theorem 3-7 Alt Int angle (converse)If two lines in a aircraft are cut by a transversal so the a pair of alternating interior angles is congruent, climate the 2 lines room parallel.
Postulate 3-2 Parallel PostulateTwo nonvertical lines have actually the exact same slope if and also only if they space parallel.
Postulate 3-3 Perpendicular PostulateTwo nonvertical lines space perpendicular if and also only if the product of their slopes is -1.
Theprem 2-1 Segment CongruenceCongruence of segment is reflexive, symmetric, and transitive
Theorem 2-2 LP complement TheoremIf 2 angle for a direct pair, climate they are supplementary angles.
Theorem 2-3 edge CongruenceCongruence of angles is reflexive, symmetric, and also transitive.
Theorem 2-4 Supplementary AnglesAngles supplementary come the exact same angle or to congruent angles are congruent.

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Theorem 2-5 security AnglesAngles complementary come the exact same angle or come congruent angles space congruent.
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