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Larson Geometry Reference – Chapter 3
Definitions
Term/Concept
Description
1 & 7
2 &8
*Alternate Exterior Angles
1
2
8
7
4 & 6
3 &5
*Alternate Interior Angles
4
6
4 & 5
3 & 6
*Consecutive Angles
(Consecutive Interior Angles)
4
3
5
1 & 5
4 &8
2 &6
3 &7
*Corresponding Angles
3
5
6
1
2
4
5
8
given a segment AB, start at point A and move to point B along
A proof written in paragraph form.
Coplanar lines that never intersect.
Lines that intersect at right angles.
Two planes that never intersect.
Non-coplanar lines that never intersect.
The ratio of the vertical change (rise) to horizontal change (run) between any two points on a
line. The slope m of a line containing two points with coordinates (x 1, y1) and (x2, y2) is given
Paragraph Proof
*Parallel Lines
*Perpendicular Lines
Parallel Planes
*Skew lines
*Slope of line
by the formula: m

y 2  y1
, where x1  x2.
x 2  x1
A line that intersects two or more coplanar lines.
*Transversal
k
Lines m and n are parallel. (m ∥ n.)
Lines m and k are skew lines.
m
U
7
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.
A segment that represents moving a specific distance in a specific direction. It is also a quantity
that has length and direction. Also known as a vector. For example, in a coordinate plane
Distance Between a Point and a
Line
Directed Line Segment
T
3
6
n
Planes T and U are parallel planes. (T ∥ U)
Lines k and n are intersecting lines.
Larson Geometry Reference – Chapter 3
Postulates
Postulate
Corresponding Angles
Corresponding Angles
Converse
Parallel Postulate
Perpendicular Postulate
Slope of Parallel Lines
Slopes of Perpendicular
Lines
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent
If two lines are cut by a transversal so that the corresponding angles is congruent, then the lines are
parallel.
If there is a line and a point not on the line, then there exists exactly one line through the point that is
parallel to the given line
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.
In a coordinate plane, two non-vertical lines are parallel if and only if they have the same slope.
In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes
is –1. That means that the slopes are negative reciprocals of each other.
Theorems
Theorems
*Alternate Interior Angles
Alternate Interior Angle
Converse
*Alternate Exterior Angles
Alternate Exterior Angle
Converse
Complementary Adjacent
Angles
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent,
then the two lines are parallel.
If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent
If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent,
then the two lines are parallel.
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
A
If BA  BC , then 1 and 2 are complementary.
1
2
B
*Consecutive Interior
Angles
Consecutive Interior Angles
Converse
*Corresponding Angles
Corresponding Angles
Converse
Four Right Angles
Linear Pair Perpendicular
Lines Perpendicular to a
Transversal
Parallel Line Transitivity
Perpendicular Transversal
Theorem
C
If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are
supplementary.
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles are
supplementary, then the two lines are parallel.
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent
If two lines are cut by a transversal so that the corresponding angles is congruent, then the lines are
parallel.
If two lines are perpendicular, then they intersect to form four right angles.
If two lines intersect to form a linear pair of congruent angles then the lines are perpendicular.
In a plane, if two lines are perpendicular to the same line, then they are parallel
If two lines are parallel to the same line, then they are parallel to each other.
In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.