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parallel lines

do not intersect, coplanar

skew lines

do not intersect, not coplanar

parallel planes

do not intersect

parallel postulate

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

perpendicular postulate

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

transversal

a line that intersects two or more coplanar lines at different points

corresponding angles

2 angles in corresponding positions relative to the 2 lines (w/ transversal)

alternate interior angles

2 angles between 2 lines and on opposite sides of a transversal

alternate exterior angles

2 angles that lie outside 2 lines and on opposite sides of a transversal

consecutive interior angles (same-side interior angles)

2 angles between 2 lines and on the same side of a transversal

corresponding angles postulate

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

alternate interior angles theorem

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

alternate exterior angles theorem

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

consecutive interior angles theorem

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

corresponding angles converse

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

alternate interior angles converse

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

alternate exterior angles converse

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

consecutive interior angles converse

If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.

transitive property of parallel lines

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

paragraph proof

statements and reasons written in sentences

slope

ratio of vertical change (rise) to horizontal change (run) between any two points on the line

slope equation

m= rise/run = change in y / change in x = (y2-y1) / (x2-x1)

negative slope

falls from left to right

positive slope

rises from left to right

zero slope

horizontal

undefined slope

vertical

slopes of parallel lines postulate

In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope.

slopes of perpendicular lines postulate

In a coordinate plane, two non-vertical lines are perpendicular if and only if the products of their slopes equals -1 (slopes of perpendicular lines are negative reciprocals). Horizontal lines are perpendicular to vertical lines.

slope-intercept form

y = mx + b

m is the slope; b is the y-intercept

m is the slope; b is the y-intercept

standard form

Ax +By = C when A & B are not both zero

linear pair perpendicular lines theorem

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

four right angles theorem

If two lines are perpendicular, then they intersect to form four right angles.

complementary adjacent acute angles theorem

If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

perpendicular transversal theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

lines perpendicular to a transversal theorem

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

distance from a point to a line

the length of the perpendicular segment from the point to the line (shortest distance)