Term | Definition |
parallel lines | coplanar lines that do not intersect |
skew lines | are noncoplanar; they are not parallel and do not intersect |
Alternate Interior Angles | nonadjacent interior angles that lie on the opposite side of the transversal |
same side interior angles | interior angles that lie on the same side of the transversal |
corresponding angles | lie on the same side of the transversal T and in corresponding postions |
alternate exterior angles | nonadjacent exterior angles that lie on the opposite side of the transversal |
Postulate 1-3
Same Side interior angles postulate | if a transversal intersects two parallel lines, then the same side interior angles are supplementary |
Theorem 3-1
alternate interior angles theorem | if a transversal intersects two parallel lines, then the alternate interior angles are congruent |
Theorem 3-2
corresponding angles theorem | if a transversal intersects two parallel lines, then the corresponding angles are congruent |
alternate exterior angles theorem | if a transversal intersects two parallel lines, the alternate exterior angles are congruent |
converse of the corresponding angles theorem | if two lines and a transversal form corresponding angles that are congruent, then the lines are parallel |
converse of the alternate interior angles theorem | if 2 lines and a transversal form corresponding angles that are congruent, then the 2 lines are parallel |
converse of same side interior angle | if 2 lines and a transversal form same side interior angles that are supplementary, then the 2 lines are parallel |
Theorem 3-7
Converse of alternate exterior angles theorem | if 2 lines and a transversal form alternate exterior angles that are congruent, then the 2 lines are parallel. |
Theorem 3-8 | if two lines are parallel to the same line, then they are parallel to each other |
Theorem 3-9 | in a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other |
Theorem 3-10 | in a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other |
Postulate 3-2
Parallel postulate | through a point not on a line, there is one and only one line parallel to that given line |