Ch 3
Parallel planes - Planes that don’t intersect.
Parallel lines - Lines that don’t intersect.
Segments and rays are parallel if they are contained in parallel lines.
Skew lines - lines that not coplanar and don’t intersect.
Three ways to determine a unique plane
Three non-collinear points
Pair of parallel lines
Pair of intersecting lines
Parallel Postulate - If there is a line and a point that is not on the line, then there is exactly one line through the point parallel to the given line.
Perpendicular Postulate - If there is a line and a point that is 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 in two different points.
When two lines are intersected by a transversal 8 angels are formed and they have different names based on their location. Some of them are:
Alternate interior angles
Alternate exterior angles
Consecutive interior of same side angles
Corresponding angles
Parallel line and transversal relationships
Parallel lines > corresponding angles are congruent
Parallel lines > alternate interior angles are congruent
Parallel lines > alternate exterior angles are congruent
Parallel lines > consecutive interior angles are supplementary
Other rules
If two lines are parallel then they are always coplanar.
If two lines are not coplanar then they never intersect.
If three lines intersect at one point then they are sometimes coplanar.
If two lines are skew to a third then they are sometimes skew to each other.
If two lines are parallel to the same lines, then they are parallel to each other.
Proving lines are parallel
Corresponding angles are congruent > parallel lines
Alternate interior angles are congruent > parallel lines
Alternate exterior lines are congruent > parallel lines
Consecutive interior angles are supplementary > parallel lines