Perpendicular Lines

1. Perpendicular Lines Geometry CP2(Holt 3-4) K.Santos

2. Perpendicular Bisector Perpendicular bisector of a segment is a line perpendicular to a segment at the segment’s midpoint. (could be a segment or ray) s M t Line s is perpendicular to line t at it’s midpoint M

3. Distance from a point to a line The shortest segment from a point to a line is perpendicular to the line. Distance form a point to a line is the length of the perpendicular segment from the point to the line.

4. Theorem (3-4-1) If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular. Given: <1 and < 2 are a linear pair n Then: m ⊥ n 1 2 m

5. Perpendicular Transversal Theorem (3-4-2) In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line. a b Given: a||b t┴a t Then: t ┴b

6. Theorem (3-4-3) Theorem: If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other. Given: a┴ t a b┴t Then: a||b b t

7. Theorem If two coplanar lines are parallel to the same line, then they are parallel to each other. t Given: a ||b a b ||c b Then: a || c c

8. Example: Use the picture at the right to answer the questions below: C P B x – 8 12 Name the shortest segment from point A to . Write and solve an inequality for x. AC > AP x – 8 > 12 x > 20

9. Example Given the information below what can you conclude about lines a and d? a ||b a b┴c c||db a ___ d? cd Draw a picture with all the line in it and then make a conclusion about lines a and d. a ┴ d