SIMPLE TERMS
Parallel Lines
Two lines in the same plane which never intersect are called parallel lines. We say that two line segments are parallel if the lines that they lie on are parallel. If line 1 is parallel to line 2, we write this as
line 1 || line 2
When two line segments DC and AB lie on parallel lines, we write this as
segment DC || segment AB.
Example: Lines 1 and 2 below are parallel.
Example: The opposite sides of the rectangle below are parallel. The lines passing through them never meet.
Transversal
is a line that intersects two or more (often) parallel lines. When the lines are parallel, a transversal produces several congruent and several supplementary angles. When three lines in general position that form a triangle are cut by a transversal, the lengths of the six resulting segments satisfy Menelaus' theorem.
Alternate Exterior Angles
In the drawing below, angles 1 and 8 are alternate exterior angles, as are angles 2 and 7. Alternate exterior angles are congruent. Formally, alternate exterior angles are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.
by a transversal |  |
Alternate Interior Angles In the drawing below, angles 3 and 6 are alternate interior angles, as are angles 4 and 5. Alternate interior angles are congruent. Formally, alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal.
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Corresponding angles
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1 and