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
Alternate Exterior Angles: 1 & 8 ; 2 & 7
Alternate Interior Angles: 3 & 6 ; 4 & 5
Consecutive Interior Angles: 4 & 6 ; 3 & 5

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.