Parallel Lines and Transversals

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then 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

Alternate Interior Angles

Nonadjacent interior angles that lie on opposite sides of the transversal

Same-Side Interior Angles

Interior angles that lie on the same side of the transversal

Corresponding Angles

Angles that lie on the same side of the transversal and in corresponding positions

Alternate Exterior Angles

Nonadjacent exterior angles that lie on opposite sides of the transversal

Same-Side Interior Angles Postulate

If a transversal intersects two parallel lines, then same-side interior angles are supplementary

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternate interior angles are congruent

Corresponding Angles Theorem

If a transversal intersects two parallel lines, then corresponding angles are congruent

Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel

Converse of the Same-Side Interior Angles Postulate

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel

Converse of the Alternate Exterior Angles Theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel

Parallel Lines

If two lines are parallel to the same line, then they are parallel to each other

Perpendicular Lines

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other

Parallel Postulate

Through a point not on a line, there is only one line parallel to the given line

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180

Remote Interior Angles

Nonadjacent interior angles

Exterior Angle

An angle formed by a side and an extension of an adjacent side

Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles

The slope (m) of a line

y2- y1/x2-x1

point-slope form

y-y1=m(x-x1)

m is the slope and (x1, y1) is a point on the line

Slopes of Parallel Lines

If two nonvertical lines are parallel, then their slopes are equal.

If the slopes of two distinct nonvertical lines are equal, then the lines are parallel.

Any two vertical lines or horizontal lines are parallel.

Slopes of Perpendicular Lines

If two nonvertical lines are perpendicular, then the product of their slopes is -1.

If the slopes of two lines have a product of -1, then the lines are perpendicular.

Any horizontal line and vertical line are perpendicular.