1. Chapter 3 Parallel and Perpendicular Lines

2. 3.1 Identify Pairs of Lines and Angles  Parallel lines- ( II ) do not intersect and are coplanar  Parallel planes- do not intersect  Skew lines- do not intersect and are NOT coplanar

3. 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.

4. 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.

5.  Transversal- a line that intersects two or more coplanar lines at different points

6.  Corresponding angles- 2 angles in the same corresponding position relative to the 2 lines  Alternate interior angles- 2 nonadjacent interior angles on opposite sides of the transversal  Alternate exterior angles- 2 exterior angles on opposite sides of the transversal  Consecutive interior angles (same side interior)- 2 interior angles on the same side of the transversal

7.  Corresponding  Alternate interior  Alternate exterior  Consecutive interior

8. Example

9. 3.2 Using Parallel Lines and Transversals  Corresponding Angles Postulate- If 2 parallel lines are cut by a transversal, then corresponding angles are congruent.

10.  Alternate Interior Angles Theorem- If 2 parallel lines are cut by a transversal, then alternate interior angles are congruent.  Alternate Exterior Angles Theorem- If 2 parallel lines are cut by a transversal, then alternate exterior angles are congruent.

11.  Consecutive Interior Angles Theorem- If 2 parallel lines are cut by a transversal, then consecutive interior angles are supplementary.

12.  Perpendicular Transversal Theorem- If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.

13. Prove the Alternate Interior Angles Theorem

14. Example

15. 3.3 Proving Lines are Parallel  Corresponding Angles Converse (Postulate)- If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

16. Theorems  Alternate 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.

17.  Consecutive Interior Angles Converse - If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.

18.  Transitive Property of Parallel Lines- If two lines are parallel to the same line, then they are parallel to each other.

19. 2-column proof of Alternate Interior Angles Converse

20. 3.4 Find and Use Slopes of Lines  Slope, m = or  Steeper slopes have higher absolute values.

21. Example  Line k passes through (0,3) and (5,2). Graph the line perpendicular to k and passes through the point (1,2). Find the equation of the perpendicular line.

22. Example  Graph using the x and y intercept: 3x + 4y = 12

23. Example  Your gym membership has a one time initial fee and a monthly fee.  2 months total spent = $ 231  5months total spent = $ 363  Write an equation in slope intercept form to represent the cost of the membership.  What does the slope represent?  What does the y intercept represent?

24. 3.5 Write and Graph Equations of Lines  Write the equation of the line in slope intercept form.

25. Example  Write the equation of the line passing through ( -1, 1) and parallel to y = 2x – 3.

26. Example  Write the equation of the line passing through ( 2, 3) and perpendicular to y = ½ x + 2.

27. Example  Write the equation of the line that is the perpendicular bisector of the line segment with endpoints: P( -4, 3 ) Q (4, -1).

28. 3.6 Prove Theorems about Perpendicular Lines  If 2 lines are perpendicular, then they intersect to form 4 right angles.  If 2 lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.  If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

29. Find the distance between a point and a line  Line m contains (0, -3) and (7, 4). P (4, 3)

30. Find the distance between 2 parallel lines  Line j: y = 5x – 22  Line m: y = 5x + 4