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3.7: Chapter 3 Review

Difficulty Level: At Grade Created by: CK-12

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 3-1
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 3-2
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_2-x_1)^2 + (y_2-y_1)^2}\end{align*}d=(x2x1)2+(y2y1)2.

Review

Find the value of each of the numbered angles below.

Texas Instruments Resources

In the CK-12 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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CK.MAT.ENG.SE.1.Geometry-Basic.3.7