__Chapter 3 Notes__

** Parallel lines**—are coplanar and do not
intersect

** Perpendicular lines**—are coplanar and
intersect to form four 90 degree angles.

** Skew lines**—are not coplanar and do not
intersect

** Parallel planes**—do not intersect

__
__

** Transversal**—a line that intersects two or
more coplanar lines. (line t)

** Corresponding angles**—angles in
corresponding positions

** Alternate Exterior angles**—lie outside the
two lines (a and b) on opposite sides of the transversal (line t)

** Alternate Interior angles**—lie between the
two lines (a and b) on opposite sides of the transversal (line t)

** Consecutive Interior angles**—lie between the
two lines (a and b) on the same side of the transversal (line t)
These are also know as

__Section
3.2 Angles and Parallel Lines
__

**Postulate 3.1:
(The Corresponding Angles Postulate) **

If two ** parallel** lines are
cut by a
transversal,

then

**Theorem 3.1: **
*(The Alternate Interior Angles Theorem)*

If two ** parallel** lines are
cut by a
transversal,

then

__Theorem 3.2: __*(The Consecutive Interior Angles Theorem)*

If two ** parallel** lines are cut by a
transversal,

then

**Theorem 3.3: **
*(The Alternate Exterior Angles Theorem)*

If two ** parallel** lines are
cut by a
transversal,

then

**Theorem 3.4**:
** (The Perpendicular Transversal Theorem)** If a line is

An angled transversal???

**Triangle Sum Theorem:**

The sum of the measures of the angles of a triangle is 180 degrees.

**Postulate 3.4: ** *
(The Corresponding Angles Converse)*

If
lines are cut
by a transversal so that a pair of **
Corresponding Angles** are
congruent,

then the lines are parallel.

**Theorem 3.5: ***(The
Alternate Exterior Angles Converse)*

If
lines are cut by a transversal so that a pair of **
Alternate Exterior Angles** are
congruent,

then the lines are parallel.

**Theorem 3.6: ***(The
Consecutive Interior Angles Converse)*

If
lines are cut by a transversal so that a pair of **
Consecutive Interior Angles** are

then the lines are parallel.

**Theorem 3.7: ***(The
Alternate Interior Angles Converse)*

If
lines are cut by a transversal so that a pair of **
Alternate Interior Angles** are
congruent,

then the lines are parallel.

**Theorem 3.8: ***(The
two perpendiculars are parallel theorem)*

If
two lines are perpendicular to the same third line,

then the two lines are parallel.

__Section 3.6 Perpendiculars and
Distance
__

The distance from **a line to a point not
on the line **is the length of the segment perpendicular to the line from the
point.

The distance between two parallel lines is the length of the segment from a point on one line to the other line in a perpendicular direction.

In a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other.