Angle Relationships

Parallel Lines

coplanar lines that never intersect

Vertical Pair

Each of the pairs of opposite angles made by two intersecting lines. (Vertical angles are CONGRUENT)

Transversal

a line that intersects 2 or more lines (line t is a transversal)

Parallel Postulate

If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.

Corresponding Angles

The angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal. (Corresponding Angles are CONGRUENT)

Skew Lines

noncoplanar lines that do not intersect

Parallel Planes

planes that never intersect

Linear Pair

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees. (Linear angles are SUPPLEMENTARY)

Alternate Exterior Angles

Alternate exterior angles are two angles that are on the exterior of and , but on opposite sides of the transversal. ... Converse of the Alternate Exterior Angles Theorem: If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel. (Alternate Interior Angles are CONGRUENT)

Alternate Interior Angles

Alternate interior angles are formed when a transversal passes through two lines. The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal. (Alternate Interior Angles are CONGRUENT)

Same Side Interior or Consecutive Interior Angles

The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary, or add up to 180 degrees. (Same Side Interior Angles are SUPPLEMENTARY)

If: -corresponding angles are congruent, -alternate exterior angles are congruent, -same-side interior angles are supplementary, -alternate interior angles are congruent, -two lines are perpendicular to the same line,

Then: -the lines are parallel.

Same Side Exterior or Consecutive Exterior Angles

When parallel lines are cut by a transversal line, same-side exterior angles are formed, which are outside of the parallel lines and on the same side of the transversal line. The theorem states that when parallel lines are cut by a transversal line, the same-side exterior angles are supplementary. (Same Side Exterior Angles are SUPPLEMENTARY)