Parallel and Perpendicular Lines Notes Unit 4 Parallel and Perpendicular Lines Distance and Midpoint Equations for Lines

Definition of Parallel Lines (//) Two lines that lie in the same plane that never intersect are called parallel. Lines m & n are parallel

Definition of Skew Lines Two lines are skew if they do not intersect and do not lie in the same plane. Lines m & k are skew

Definition of Parallel Planes Two planes that do not intersect. Planes T & U are parallel

Definition of Perpendicular Lines Perpendicular lines are lines that intersect to form a right angle. Line CD and Line DE are perpendicular

Definition of Perpendicular Planes Planes that intersect to form a right angle. Planes ABC and ABG are perpendicular.

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. There is exactly one line through P parallel to line l.

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. There is exactly one line through P perpendicular to line l.

Corresponding Angles postulate Two lines cut by a transversal are parallel if and only if the pairs of corresponding angles are congruent.

Alternate Interior Angles Theorem Two lines cut by a transversal are parallel if and only if the pairs of alternate interior angles are congruent.

Alternate exterior angles theorem Two lines but by a transversal are parallel if and only if the pairs of alternate exterior angles are congruent.

Consecutive Interior Angles Theorem Two lines cut by a transversal are parallel if and only if the pairs of consecutive interior angles are supplementary.

Example Find the value of x.

Example Find the value of x. The picture may not be drawn to scale. (3x + 5)o (7x – 15)o

Transitive Property of Parallel Lines If two lines are // to the same line, then they are // to each other.

Perpendicular Transversal Theorem If a transversal is  to one of two // lines, then it is  to the other. If line j  line h and line h and line k are //, then line j  line k

Lines Perpendicular to a Transversal Theorem In a plane, if 2 lines are  to the same line, then they are // to each other. If lines m & n are both  to line p, then lines m & n are //.

Slope Formula: Slope = y2 – y1 the change in y divided by the change in x Formula: Slope = y2 – y1 x2 – x1

Postulate – Slope of Parallel Lines In the same plane, // lines have = slopes.

Postulate – Slope of Perpendicular Lines In the same plane,  lines have slopes that are negative reciprocals of each other.

Definition – Distance from a point to a Line The distance between a point and a line must be measured with a  segment from the point to the line.

Example Graph the line y = x + 1. What point on the line is the shortest distance from the point (4, 1)? What is the distance?