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Chapter 3 Theorems/Definitions/Postulates
Slope for two points
falls left to right
rises left to right
Transitive Property of Parallel Lines
If two lines are parallel to the same line, then they are parallel to each other
Corresponding Angles Converse
If two lines are cut by a transversal so the corresponding angles are congruent, 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
Alternate Exterior Angles Converse
If two lines are cut by a transversal so the 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
Slopes of Parallel lines
two nonvertical lines are parallel if and only if they have the same slope; any two vertical lines are parallel
Slopes of perpendicular lines
two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Horizontal lines are perpendicular to vertical lines.
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular
If two lines are perpendicular, then they intersect to form four right angles
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Lines Perpendicular to a Transversal Theorem
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other