How can we help?

You can also find more resources in our Help Center.

Chapter 3 VPTF

STUDY
PLAY
parallel lines
Two lines that do not intersect and are coplanar
skew lines
Lines that do not intersect are not coplanar.
parallel planes
Two planes that do not intersect
transversal
a line that intersects two or more coplanar lines at different points.
corresponding angles
Two angles that are formed by two lines and a transversal and occupy corresponding positions.
alternate interior angles
Two angles that are formed by two lines and a transversal and lie between the two lines and on opposite sides of the transversal.
alternate exterior angles
Two angles that are formed by two lines and a transversal and lie outside the two lines and on opposite sides of the transversal.
consecutive interior angles
Two angles that are formed by two lines and a transversal and lie between the two lines and on the same side of the transversal. Also called same-side interior angles.
paragraph proof
A type of proof written in paragraph form.
slope
The slope m of a non-vertical line is the ratio of the vertical change (the rise) to horizontal change (the run) between any two points on the line.
slope-intercept form
A linear equation written in the form y = mx + b where m is the slope and b is the y-intercept of the equation's graph.
standard form of a linear equation
A linear equation written in the form Ax + By = C, where A, B, and C are real numbers and A and B are not both zero.
distance from a point to a line
The length of the perpendicular segment from the point to the line.
Parallell 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.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Corresponding Angles Converse
If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Slopes of Parallell Lines
In a coordinate plane, two non vertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel.
Slopes of Perpendicular Lines
In a coordinate plane, two non vertical lines are perpendicular if and only if the product of their slopes is -1. Horizontal lines are perpendicular to vertical lines.
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.
Alternative 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.
If two lines intersect to form a linear pair of congruent angles
then the lines are perpendicular.
It two lines are perpendicular
then they intersect to form four right angles.
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 plan,e if two lines are perpendicular to the same line, then they are parallel to each other.