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Parallel Lines and Planes
Chapter 3
Pre-AP Geometry
Topics
3.1 Definitions
3.2 Properties of Parallel Lines
3.3 Proving Lines Parallel
3.4 Applying Parallel Lines to Polygons
3.5 Angles of a Polygon
3.6 Inductive Reasoning
Definitions
Lesson 3.1
Pre-AP Geometry
Objectives
1. Distinguish between intersecting lines, parallel
lines, and skew lines.
2. State and apply the theorem about the
intersection of two parallel planes by a third
plane.
3. Identify the angles formed when two lines are
cut by a transversal.
Parallel lines
Parallel Lines are coplanar lines that never
intersect. Two non-vertical lines are parallel if
and only if they have the same slope.
Skew lines
Two lines that do not intersect but are not
parallel. They are lines that are not both in the
same plane.
Transversal
A line that passes through two or more other
coplanar lines at different points.
Alternate interior angles
Alternate Interior Angles are created where a
transversal crosses two (usually parallel) lines.
Each pair of these angles are inside the parallel
lines, and on opposite sides of the transversal.
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Same-side interior angles
Two interior angles on the same side of the
transversal.
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Corresponding Angles
When two lines are crossed by another line (the
transversal), the angles in matching corners are
called corresponding angles.
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Parallel Planes Theorem
If two parallel planes are cut by a third plane,
then the lines of intersection are parallel.