1. LESSON FOUR: SEGMENTS AND SKEW LINES AND VECTORS…OH MY!!!

2. SEGMENTS The last new thing we will discuss about segments will be the segment addition postulate. Point B is between points A and C if and only if A, B and C are collinear and AB + BC = AC. BAC

3. SEGMENTS A midpoint is a point that lies directly in the middle of a segment. If M is the midpoint of AB then AM = ½ AB

4. SEGMENTS On the segment below, construct a midpoint. AB

5. SEGMENTS When you have to find a midpoint on a coordinate plane, we can use the midpoint formula. On a coordinate plane, the midpoint of the segment with endpoints (x 1, y 1 ) and (x 2, y 2 ) has coordinates ((x 1 + x 2 )/2, (y 1 + y 2 )/2 ).

6. SEGMENTS TRY THE MIDPOINT FORMULA!!!

7. SPECIAL LINES Seeing as how we are now dealing with planes, we must refine our definition of parallel lines. Parallel lines are coplanar lines that do not intersect.

8. SPECIAL LINES Noncoplanar lines are called skew lines. They DO NOT intersect, but they ARE NOT parallel.

9. SPECIAL LINES Sometimes you will be asked to PROVE that certain lines are perpendicular or parallel. Knowing how slopes relate is the key here.

10. SPECIAL LINES Nonvertical parallel lines have the same slope. Nonvertical perpendicular lines have slopes with a product of -1.

11. SPECIAL LINES Parallel Postulate – Through a given point P, not on line l, exactly one line may be drawn parallel to line l.

12. SPECIAL LINES Construct a line parallel to l and through P. THIS WILL SHOW YOU HOW P l

13. VECTORS Vectors are used to describe a straight-line path from point A to point B. What makes the path from A to B different than A to C or A to D? A B D C

14. VECTORS The length of a vector is the distance between A and B. The direction of a vector is measured counterclockwise from the horizontal (positive x-axis).

15. VECTORS Equal vectors are ones that have the same direction AND length. A vector sum means one vector followed by another. See below. A F E D C B

16. VECTORS Thus, AB + BC + CD + DE + EF = AF Is the angle of AF positive or negative? A F E D C B