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Geometry
Study Guide Chapter 3
I.
Terms
A. Parallel Lines: Coplanar lines that do not intersect
B. Skew Lines: Noncoplanar lines that do not intersect
C. Transversal: A line that intersects two or more lines at different
points
D. Perpendicular Lines: Two lines whose intersection forms right angles
E. Slope-Intercept Form: y = mx + b
F. Standard Form: Ax + By = C
G. y-intercept: Point on a graph where a line crosses the y-axis
H. x-intercept: Point on a graph where a line crosses the x-axis
II.
Angle Types (Use the diagram as a point of reference)
1
2
3
4
5
6
7
8
A. Corresponding Angles
1. A Pair of angles in the same position on a transversal and the lines
the transversal is cutting across
2. Examples: 1 & 5; 2 & 6; 3 & 7; 4 & 8
B. Alternate Interior Angles
1. A pair of angles on opposite sides of a transversal and on the
inside of the two lines cut by the transversal
2. Examples: 3 & 6; 4 & 5
C. Alternate Exterior Angles
1. A pair of angles on opposite sides of a transversal and on the
outside of the two lines cut by the transversal
2. Examples: 1 & 8; 2 & 7
D. Consecutive Interior Angles
1. A pair of angles on the same side of a transversal and on the inside
of the two lines cut by the transversal
2. Examples: 3 & 5; 4 & 6
III.
Postulates and Theorems
A. Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then corresponding
angles are congruent
B. Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then alternate interior
angles are congruent
C. Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then alternate exterior
angles are congruent
D. Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then consecutive interior
angles are supplementary
E. Converse of Alternate Interior Angles Theorem
If alternate interior angles are congruent, then the two lines cut by the
transversal are parallel
F. Converse of Alternate Exterior Angles Theorem
If alternate exterior angles are congruent, then the two lines cut by
the transversal are parallel
G. Converse of Consecutive Interior Angles Theorem
If consecutive interior angles are supplementary, then the two lines
cut by the transversal are parallel
H. Corresponding Angles Converse (Postulate)
If corresponding angles are congruent, then the two lines cut by the
transversal are parallel
I. Transitive Property of Parallel Lines (Theorem)
If two lines are parallel t the same line, then they are parallel to each
other
IV.
Slope
A. Formula
𝑅𝑖𝑠𝑒
m = 𝑅𝑢𝑛 =
𝐶ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑦
𝐶ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑥
=
𝑦2−𝑦1
𝑥2−𝑥1
B. Slope Relationships
1. Parallel Lines: Slopes are the same, intercepts are different
a. Example: y = 2x + 7 and y = 2x – 9 are Parallel Lines
2. Perpendicular Lines: Slopes are opposite reciprocals
2
3
a. Example: y = 3x + 3 and y = − 2x – 6 are Perpendicular Lines