3.7: Chapter 3 Review
Difficulty Level: At Grade
Created by: CK12
Keywords and Theorems
 Parallel
 When two or more lines lie in the same plane and never intersect.
 Skew Lines
 Lines that are in different planes and never intersect.
 Parallel Postulate
 For a line and a point not on the line, there is exactly one line parallel to this line through the point.
 Perpendicular Line Postulate
 For a line and a point not on the line, there is exactly one line parallel to this line through the point.
 Transversal
 A line that intersects two distinct lines. These two lines may or may not be parallel.
 Corresponding Angles
 Two angles that are in the “same place” with respect to the transversal, but on different lines.
 Alternate Interior Angles

Two angles that are on the interior of \begin{align*}l\end{align*}
l and \begin{align*}m\end{align*}m , but on opposite sides of the transversal.
 Alternate Exterior Angles

Two angles that are on the exterior of \begin{align*}l\end{align*}
l and \begin{align*}m\end{align*}m , but on opposite sides of the transversal.
 Same Side Interior Angles
 Two angles that are on the same side of the transversal and on the interior of the two lines.
 Corresponding Angles Postulate
 If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
 Alternate Interior Angles Theorem
 If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
 Alternate Exterior Angles Theorem
 If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
 Same Side Interior Angles Theorem
 If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
 Converse of Corresponding Angles Postulate
 If corresponding angles are congruent when two lines are cut by a transversal, then the lines are parallel.
 Converse of Alternate Interior Angles Theorem
 If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
 Converse of the Alternate Exterior Angles Theorem
 If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.
 Converse of the Same Side Interior Angles Theorem
 If two lines are cut by a transversal and the consecutive interior angles are supplementary, then the lines are parallel.
 Parallel Lines Property
 The Parallel Lines Property is a transitive property that can be applied to parallel lines.
 Theorem 31
 If two lines are parallel and a third line is perpendicular to one of the parallel lines, it is also perpendicular to the other parallel line.
 Theorem 32
 If two lines are parallel and a third line is perpendicular to one of the parallel lines, it is also perpendicular to the other parallel line.
 Distance Formula

\begin{align*}d = \sqrt{(x_2x_1)^2 + (y_2y_1)^2}\end{align*}
d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√ .
Review
Find the value of each of the numbered angles below.
Texas Instruments Resources
In the CK12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9688.
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Tags:
Alternate Exterior Angles Theorem
Alternate Interior Angles Theorem
angles
(18 more)
CK.MAT.ENG.SE.1.GeometryBasic.3
CK.MAT.ENG.SE.2.Geometry.3
coordinate plane
Corresponding Angles Postulate
distance formula
equations of lines
Lines
Parallel Line Postulate
Parallel Lines
Perpendicular Line Postulate
perpendicular lines
planes
proofs
proving parallel lines
Same Side Interior Angles Theorem
slopes
the Distance Formula
transversals
Subjects:
Date Created:
Feb 22, 2012
Last Modified:
Feb 03, 2016
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