1. Notes 3.4
Perpendicular Lines

2. Perpendicular Bisector
A line that is perpendicular to, and bisects, a segment.
Segments intersect at right angles.

3. Distance from a point to a line
The shortest distance from a point to a line is ALWAYS perpendicular to the line.

4. Example 1: Distance From a Point to a Line
A. Name the shortest segment from point A to BC. AP
B. Write and solve an inequality for x.
AC > AP
AP is the shortest segment.
x – 8 > 12
Substitute x – 8 for AC and 12 for AP.
+ 8
Add 8 to both sides of the inequality.
x > 20

5. Theorems
If 2 intersecting lines form a linear pair of congruent angles, then the lines are perpendicular.
If a transversal is perpendicular to one line, then it is perpendicular to a line parallel to that line.
If 2 lines are perpendicular to the same line, then the 2 lines are parallel.

6. Examples 2 and 3
2. Write and solve an inequality for x.
2x – 3 < 25
x < 14
3. Solve to find x and y in the diagram.
10x = 90
x = 9, y = 4.5