transversal
line that intersects two or more coplanar lines at distinct points
parallel lines
coplanar lines that do not intersect
skew lines
non-coplanar lines that do not intersect
parallel planes
planes that do not intersect
alternate interior angles
nonadjacent interior angles that lie on opposite sides of the transversal
alternate exterior angles
nonadjacent exterior angles that lie on opposite sides of the transversal
corresponding angles
lie on the same side a the transversal and in corresponding positions
same side interior angles
interior angles that lie on the same side of the transversal (also called consecutive interior angles)
alternate interior angles theorem
if a transversal intersects two parallel lines, alternate interior angles are congruent.
same side interior angles theorem
if a transversal intersects two parallel lines, same side interior angles are supplementary
corresponding angles postulate
if a transversal intersects two parallel lines corresponding angles are congruent
alternate exterior angle theorem
if a transversal intersects two parallel lines alternate exterior angles are congruent
Converse of the Corresponding Angles Postulate
if corresponding angles are congruent, then the lines are parallel
Converse of the Alternate Interior Angles Theorem
if alternate interior angles are congruent, then the lines are parallel
Converse of the Alternate Exterior Angles Theorem
if alternate exterior angles are congruent, then the lines are parallel
Converse of the same side interior angles theorem
if same side interior angles are supplementary, then the lines are parallel
flow proof
logical argument using arrows and boxes to show the connections between statements
if two lines are parallel to the same line...
then they are parallel to each other
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
through a point not on a line,
there is exactly one line parallel to the given line
through a point not on a line
there is exactly one line perpendicular to the given line
Triangle Sum Theorem
the sum of the interior angles of a triangle is 180 degrees
exterior angle of a polygon
an angle formed by a side and am extension of an adjacent side
remote interior angles
for an exterior angle, these are the angles that are non-adjacent and interior to it
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
slope of a line
the ratio of vertical change (rise) to the horizontal change (run) between any two points
slope - intercept form
an equation for a non-vertical line in the form y=mx + b, where b is the y-intercept and m is the slope of the line
point - slope form
an equation for a non-vertical line in the form y - y1 = m ( x - x1) where (x1, y1) is a point on the line and m is the slope of the line
if two non-vertical 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 any two horizontal lines...
are parallel
if two non-vertical lines are perpendicular ...
then the product of their slopes is -1
(negative reciprocals)
if two lines have slopes that are negative reciprocals of each other...
then the lines are perpendicular
any horizontal and any vertical line will be...
perpendicular to each other