Lines and Angles

Corresponding Angles

Angles that are in the same position. When a transversal intersects two lines, these angles are on the same side of the transversal and on is interior and the other is exterior

Converse of the Alternate Exterior Angles Theorem

If two lines are cut by a transversal so that the alternate exterior angles formed by the transversal are congruent, then the lines are parallel.

Converse of Alternate Interior Angles Theorem

If two lines are cut by a transversal so that the alternate interior angles formed by the transversal are congruent, then the lines are parallel.

Converse of Corresponding Angles Postulate

If two lines are cut by a transversal so that the corresponding angles formed by the transversal are congruent, then the lines are parallel.

Converse of Same-Side Interior Angles Theorem

If two lines are cut by a transversal so that the same-side interior angles formed by the transversal are supplementary, then the lines are parallel.

Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the alternate exterior angles formed by the transversal are congruent.

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the alternate interior angles formed by the transversal are congruent.

Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then the corresponding angles formed by the transversal are congruent.

Same-Side Interior Angles Theorem

If two parallel lines are cut by a transversal, then the same-side interior angles formed by the transversal are supplementary.

Same-Side Interior Angles

Pairs of angles formed when a third line (a transversal) crosses two other lines. These angles are on the same side of the transversal and are between the other two lines. When the two other lines are parallel, same-side interior angles are supplementary.

Same-Side Exterior Angles

Pairs of angles formed when a third line (a transversal) crosses two other lines. These angles are on the same side of the transversal and are outside the other two lines. When the two other lines are parallel, same-side exterior angles are supplementary.

between

Point B is "between" A and C if it lies on the segment AC

colinear

Points that lie on the same line

Transversal

A line that crosses two or more lines.

Perpendicular Bisector

A perpendicular line or segment that passes through the midpoint of a segment.

Parallel Lines

Two lines are parallel if they lie in the same plane and they do not intersect.

Perpendicular Lines

Two lines are perpendicular if they intersect at a right angle.

Skew Lines

Two lines that do not lie in the same plane (therefore, they cannot be parallel or intersect).

Alternate Exterior Angles

When a transversal intersects two lines, these angles are on opposite sides of the transversal and are both in the exterior of the lines

Alternate Interior Angles

When a transversal intersects two lines, these angles are on opposite sides of the transversal and are both in the interior of the lines