Chapter 3 Theorems and Postulates Flashcards
Alternate Interior Angles Theorem
Congruent
Consecutive Interior Angles Theorem
Supplementary
Alternate Exterior Angles Theorem
Congruent
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Slopes of Parallel Lines Postulate
2 lines are parallel if they have the same slope, vertical lines are always parallel with the same slope
Slopes of Perpendicular Lines Postulate
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1.
Converse of the Corresponding Angles Postulate
If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.
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.
Alternate Exterior Angles Converse Theorem
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
Consecutive Interior Angles Converse
If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.
Alternate Interior Angles Converse
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
Perpendicular Transversal Converse
In a plane, if two lines are perpendicular to the same line, then they are parallel.
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.
Two Lines Equidistant from a Third
In a plane, if two lines are each equidistant from a third line, then the two lines are parallel to each other.
