Download RGeo Ch 3 Study Guide

Regents Geometry
Chapter 3 Study Guide
Use the following website for on-line resources (practice tests and quizzes):
http://www.glencoe.com/sec/math/geometry/geo/geo_04/
Select what you want to do and then go to Chapter 3 Parallel and Perpendicular Lines.
Chapter 3 – Parallel and Perpendicular Lines
 Definitions with images can be found using Quizlet: http://quizlet.com/24451796/familiarize/
Parallel Lines
Skew Lines
Parallel Planes
Transversal
Interior Angles
Exterior Angles
Lines in the same plane that never intersect.
Lines that do not intersect and are not in the same plane.
Planes that never intersect.
A line that intersects two or more lines in a plane at different points
Angles that lie inside parallel lines.
Angles that lie outside parallel lines.
Consecutive Interior Angles
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Angles that are on the same side of the transversal and inside
the parallel lines.
Angles that are on opposite sides of the transversal and inside
the parallel lines.
Angles that are on opposite sides of the transversal and outside
the parallel lines.
Angles that are in the same position on the parallel lines with
respect to the transversal.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, than each
pair of corresponding angles is congruent.
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of
alternate interior angles is congruent.
Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of
consecutive interior angles is supplementary (add to 180°).
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of
alternate exterior angles is congruent.
Slope of a Line Definition
The ratio of the change along the y-axis to the change along the x-axis.
Commonly referred to as "rise over run".
Slope of a Line Equation
𝒎 = 𝒙𝟐 −𝒙𝟏
Slope of a Vertical Line
Is undefined because the denominator of the slope formula (𝑥2 − 𝑥1 )
is equal to zero.
𝒚 −𝒚
𝟐
𝟏
Slope of a Horizontal Line
A Line with Positive Slope
A Line with Negative Slope
Is equal to zero because the numerator of the slope formula (𝑦2 − 𝑦1 )
is equal to zero.
Rises from left to right.
Falls from left to right.
Postulate: Slopes of Parallel Lines
Two non-vertical lines have the same slope if and only if they
are parallel. (𝑚1 = 𝑚2 ) Note: All vertical lines are parallel.
Postulate: Slopes of Perpendicular Lines Two non-vertical lines are perpendicular if and only if the
product of their slopes is equal to −1.
1
(𝑚1 𝑚2 = −1 or 𝑚1 = − 𝑚 )
2
Note: Vertical lines are perpendicular to horizontal lines.
Slope-Intercept Form of the Equation of a Line
𝑦 = 𝑚𝑥 + 𝑏
Point-Slope Form of the Equation of a Line
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
𝒚-intercept
The point where a line (or curve) intersects the 𝑦-axis.
Equation of a Horizontal Line 𝑦 = 𝑏 (Note: 𝑥-values change, 𝑦-value is constant.)
Equation of a Vertical Line
𝑥 = 𝑎 (Note: 𝑦-values change, 𝑥-value is constant.)
Postulate: Converse of Corresponding Angles
If two lines are cut by a transversal so that
corresponding angles are congruent, then the
lines are parallel.
Postulate: Converse of Alternate Exterior Angles
If two lines are cut by a transversal so that
alternate exterior angles are congruent, then
the lines are parallel.
Postulate: Converse of Alternate Interior Angles
If two lines are cut by a transversal so that
alternate interior angles are congruent, then
the lines are parallel.
Postulate: Converse of Consecutive Interior Angles
If two lines are cut by a transversal so that
consecutive interior angles are supplementary,
then the lines are parallel.