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

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

3. 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

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

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

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

7. 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.

8. 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.

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

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

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

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

13. Example
Find the value of x.

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

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

16. 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

17. 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 //.

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

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

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

21. 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.

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