Chapter 3 Notes
Section 3.1
• Parallel Lines: coplanar lines that do not intersect.
• Skew Lines: lines that are not coplanar and do not intersect.
• Transversal: a line that intersects two or more coplanar lines at different points.
• Corresponding Angles: If a transversal intersects two or more lines, angles that
occupy the same position relative to the transversal and the two lines are
corresponding angles.
• Alternate Interior Angles: If a transversal intersects two or more lines, angles that
are inside of the two lines and on opposite sides of the transversal, are alternate
interior angles.
• Alternate Exterior Angles: If a transversal intersects two or more lines, angles that
are outside of the two lines and on opposite sides of the transversal, are alternate
exterior angles.
• Consecutive Interior Angles: If a transversal intersects two or more lines, angles that
lie between the two lines and on the same side of the transversal are consecutive
interior angles.
• 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.
• 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.
Section 3.2
• Theorem 3.1: If two lines intersect to form a linear pair of congruent angles, then the
lines are perpendicular.
• Theorem 3.2: If two sides of two adjacent acute angles are perpendicular, then the
angles are complementary.
• Theorem 3.3: If two lines are perpendicular, then they intersect to form four right
angles.
Section 3.3
• Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then
the pairs of corresponding angles are congruent.
• Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are congruent.
• Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal,
then the pairs of consecutive interior angles are supplementary.
• Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal,
then the pairs of alternate exterior angles are congruent.
• Perpendicular Transversal Theorem: If a transversal is perpendicular to one of two
parallel lines, then it is perpendicular to the other.
Section 3.4
• Corresponding Angles Converse Postulate: If two lines are cut by a transversal so
that corresponding angles are congruent, then the lines are parallel.
• Alternate Interior Angles Converse Theorem: If two lines are cut by a transversal
so that alternate interior angles are congruent, then the lines are parallel.
• Consecutive Interior Angles Converse Theorem: If two lines are cut by a
transversal so that consecutive interior angles are supplementary, then the lines are
parallel.
• Alternate Exterior Angles Converse Theorem: If two lines are cut by a transversal
so that alternate exterior angles are congruent, then the lines are parallel.
Section 3.5
• Theorem 3.11: If two lines are parallel to the same line, then they are parallel to each
other.
• Theorem 3.12: In a plane, if two lines are perpendicular to the same line, then they are
parallel to each other.
Section 3.6
• Slopes of Parallel Lines Postulate: In a coordinate plane, two nonvertical lines are
parallel if and only if they have the same slope. Any two vertical lines are parallel.
• Slope-intercept form of a line: y = mx + b,
m =slope
b = y-intercept
Section 3.7
• Slopes of Perpendicular Lines Postulate: In a coordinate plane, two nonvertical
lines are perpendicular if and only if the product of their slopes is –1.
Vertical and horizontal lines are perpendicular.