Transcript 3.1_Parallel_Lines_and_Transversals_(HGEO)

Parallel Lines and
Transversals
Honors Geometry
Chapter 3, Section 1
Notes

What does it mean for two lines to be parallel?


What about lines that don’t intersect and aren’t
coplanar?


Parallel lines: Lines that do not intersect and are 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
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?


How about line a?


a&c
b&c
When a transversal
intersects two lines,
how many angles are
formed?

8 angles are formed
b
c
a
Notes

Angles formed by a transversal.







We give certain pairs of these angles special names.
Corresponding Angles: 1 & 5 ; 2 & 6 ; 3 & 7 ; 4 & 8
Exterior Angles: 1, 2, 7, & 8
Interior Angles: 3, 4, 5, 6
Alternate Exterior Angles: 1 & 7 ; 2 & 8
Alternate Interior Angles: 3 & 5 ; 4 & 6
Consecutive Interior Angles: 4 & 5 ; 3 & 6
1 2
4 3
5 6
8 7
Notes

Symbols for parallel in statements and figures


The symbol ll means is parallel to
The pink arrows on lines PQ and RS indicate that they
are parallel.
Angle Pair Names Activity

Using about ¼ of a piece of binder paper, draw three lines so that one intersects
two of the others.




Using another ¼ of a piece of binder paper, draw three lines so that one
intersects two of the others.



Color each pair of corresponding angles a different color.
Label this quarter sheet of paper “corresponding angles.”
Using another ¼ of a piece of binder paper, draw three lines so that one
intersects two of the others.




Color the exterior angles all one color
Color the interior angles all one color
Label the exterior and interior angles
Color each pair of alternate exterior angles a different color.
Color each pair of alternate interior angles a different color.
Label this quarter sheet “alternate exterior and interior angles.”
Using the final ¼ of a piece of binder paper, draw three lines so that one
intersects two of the others.


Color each pair of consecutive interior angles a different color.
Label this quarter sheet “consecutive interior angles.