1. Geometry Chapter 3, Section 1
Lines and Angles
Geometry
Chapter 3, Section 1

2. Notes What does it mean for two lines to be parallel?
Parallel lines: Lines that do not intersect and are coplanar.
What about lines that do not intersect and are not coplanar?
Skew Lines: Lines that do not intersect and are not coplanar.
What does it mean for two planes to be parallel?
Parallel Planes: planes that do not intersect.
Example: the planes containing the ceiling and floor are parallel

3. Notes 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.
Parallel lines have the same slope (line P slope = 3 and Line m slope = 3)
Tilted at the same angle
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.
Perpendicular lines have slopes that are negative reciprocals (line k slope = 4 and line Q slope = – 1/4)
At 90 degrees from each other

4. Notes Transversal: a line that intersects two or
more lines in a plane at different points.
E.g. Line c is a transversal to lines a and b.
Line b is a transversal to which two other lines?
a & c
How about line a?
b & c
When a transversal
intersects two lines,
how many angles are
formed?
8 angles are formed

5. Notes Angles formed by a transversal.
We give certain pairs of these angles special names.
Exterior Angles: 1, 2, 7, & 8
Interior Angles: 3, 4, 5, 6
Corresponding Angles: 1 & 5 ; 2 & 6 ; 3 & 7 ; 4 & 8
Congruent when the lines are parallel
Alternate Exterior Angles: 1 & 7 ; 2 & 8
Alternate Interior Angles: 3 & 5 ; 4 & 6
Consecutive Interior Angles: 4 & 5 ; 3 & 6
Supplementary when the lines are parallel

6. Notes Symbols for parallel in statements and figures
The symbol ║ means is parallel to
The pink arrows on lines PQ and RS indicate that they are parallel.

7. Parallel Line Problems
1. Find the measure of each numbered angle in the figure below.
Given:
Line GH is parallel to ray DK
Angle 6 = 75 degrees.
Angle 2 = 30 degrees.