Skew Lines
Lines that do not intersect and are not coplanar.
Parallel Lines
lines in the same plane that never intersect
Parallel Planes
Planes that do not intersect
Postulate 3.1: 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.
Postulate 3.2: 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.
Transversal
A line that intersects two or more coplanar lines at different points
Corresponding Angles
Angles formed by a transversal cutting through 2 or more lines that are in the same relative position.
Alternate Interior Angles
Angles that lie within a pair of lines and on opposite side of a transversal.
Alternate Exterior Angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
Consecutive Interior Angles
Two angles that lie between the two lines on the same side of the transversal.
Theorem 3.1: Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the pair of corresponding angles are congruent.
Theorem 3.2: Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Theorem 3.3: Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
Theorem 3.4: Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
Theorem 3.5: Corresponding Angles Converse
If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Theorem 3.6: Alternate Interior Angles Converse
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel.
Theorem 3.7: Alternate Exterior Angles Converse
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.
Theorem 3.8: Consecutive Interior Angles Converse
If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.
Theorem 3.9: Transitive Property of Parallel Lines
If two lines are parallel to the same line, then they are parallel to each other.
Distance from a Point to a Line
The length of the perpendicular segment from the point to the line.
Perpendicular Bisector
A segment, ray, line, or plane that is perpendicular to a segment at its midpoint
Theorem 3.10: Linear Pair Perpendicular Theorem
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Theorem 3.11: Perpendicular Transversal Theorem
In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
Theorem 3.12: 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.
Directed Line Segment
A segment, AB, that represents moving from point A to point B.
Theorem 3.13: Slopes of Parallel Lines
In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope.
Theorem 3.14: Slopes of Perpendicular Lines
In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1.