Math Proofs

Chapter 6

Angle

A figure formed by two rays that share a common endpoint called the vertex.

Vertex

The common endpoint of two rays that form an angle.

Ray

A part of a line that has one endpoint and extends infinitely in one direction.

Line

A straight path that extends infinitely in two directions.

Line Segment

A part of a line with two endpoints.

Adjacent Angles

Two angles that share a common vertex and a common side but do not overlap.

Vertical Angles

Two non-adjacent angles formed by two intersecting lines that are opposite each other.

Linear Pair

Two adjacent angles whose non-common sides form a straight line.

Complementary Angles

Two angles whose measures add up to 90 degrees.

Supplementary Angles

Two angles whose measures add up to 180 degrees.

Parallel Lines

Lines in the same plane that never intersect.

Perpendicular Lines

Lines that intersect to form right angles.

Transversal

A line that intersects two or more lines at different points.

Corresponding Angles

Angles that are in the same relative position when a transversal intersects parallel lines.

Alternate Interior Angles

Angles that are between the parallel lines and on opposite sides of the transversal.

Alternate Exterior Angles

Angles that are outside the parallel lines and on opposite sides of the transversal.

Same Side Interior Angles (Consecutive Interior Angles)

Angles that are between the parallel lines and on the same side of the transversal.

Same-Side Exterior Angles

Angles that are outside the parallel lines and on the same side of the transversal.

Angle Addition Postulate

If a point lies in the interior of an angle, the measure of the whole angle is the sum of the measures of its parts.

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary.

Vertical Angles Theorem

Vertical angles are congruent.

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

Same-Side Interior Angles Postulate

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

Corresponding Angles Converse

If corresponding angles are congruent, then the lines are parallel.

Alternate Interior Angles Converse

If alternate interior angles are congruent, then the lines are parallel.

Same-Side Interior Angles Converse

If same-side interior angles are supplementary, then the lines are parallel.