Chapter 3 Flashcards
Skew Lines
do not intersect and are not coplanar
Parallel Planes
Planes that don’t intersect
A line that intersects two or more coplanar lines at 2 different points
Transversal
Angles that lie between two transversals that intersect the same line
Interior Angles
An angle that lies in the region that is not between two transversals that intersect the same line
Exterior Angle
Interior Angles that lie on the same side of the transversal
Consecutive Interior Angles
Nonadjacent interior angles that lie on opposite sides of the transversal
Alternate Interior Angles
Nonadjacent exterior angles that lie on opposite sides of the transversal
Alternate Exterior Angles
Angles on the same side of the transversal, in the same position to each line
Corresponding Angles
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent
Alt Int angles Postulate
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent
Consecutive Interior Angles Postulate
If two parallel lines are cit by a transversal, each pair of consec int.
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent
Perpendicular Transversal Theorem
If a line is perpendicular to one of two parallel lines, it is perpendicular to the other
The ratio of change along the y-axis to the change along the x-axis between any two points on the line
Slope
Slope Formula
y2-y1/x2-x1
(Parallel, perpendicular) Lines have the same slope
Parallel
If two lines are perpendicular, their slopes are…
Opposite Reciprocals
Slope intercept Form
y=mx+b
Point-Slope Form
y-y1=m(x-x1)
Equation of a Horizontal Line
y=b
equation of a vertical line
x=a
Converse
switches hypothesis and conclusion
Parallel Lines
Coplanar lines that do not intersect
Converse of Corresponding Angles Postulate
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
Alternate Exterior Angles Converse
If two lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are parallel
Consecutive Interior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel
Alternate Interior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel
Perpendicular Transversal Converse
In a plane, if two lines are perpendicular to the same line, then they are parallel
Parallel Postulate
If given a line and a point not on the line, there exists exactly one line through the point that is parallel to the given line
Distance Between a Point and a Line
the distance between a line and a point not on the line is the segment perpendicular to the line from the point
Perpendicular Postulate
If given a line and a point not on the line, there is exactly one line through the point that is perpendicular to the given line
The distance between two lines measured along a perpendicular line to the lines is always the same
Equidistant
Distance Between Parallel Lines
The distance between two parallel lines is the perpendicular distance from one of the lines and any point on the other line.
Converse of Corresponding Angles Postulate
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
Alternate Exterior Angles Converse
If two lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then the lines are parallel
Consecutive Interior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel
Alternate Interior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel
Perpendicular Transversal Converse
In a plane, if two lines are perpendicular to the same line, then they are parallel
Parallel Postulate
If given a line and a point not on the line, there exists exactly one line through the point that is parallel to the given line
Distance Between a Point and a Line
the distance between a line and a point not on the line is the segment perpendicular to the line from the point
Perpendicular Postulate
If given a line and a point not on the line, there is exactly one line through the point that is perpendicular to the given line
The distance between two lines measured along a perpendicular line to the lines is always the same
Equidistant
Distance Between Parallel Lines
The distance between two parallel lines is the perpendicular distance from one of the lines and any point on the other line.
