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GEOMETRY NOTES
Lesson 3.1
Line Pairs and Transversals
Rode2010
Key words: skew lines, transversal, corresponding angles, alternate interior angles, alternate interior angles.
Review for the Lesson
Adjacent angles share a common vertex and side. What does adjacent mean?
Two angles are _____________________ angles if the sum of their measures is 180o.
Sketch a diagram for each statement:
Draw ∠ࡽࡾࡼ. Identify the vertex in your drawing.
Lines m and n intersect at point P
What is a plane? Is it a defined or undefined term?
Lesson 3.1
Two lines that lie in the same plane are considered coplanar.
l
line l and line p are coplanar
p
Two lines that lie in different planes are considered noncoplanar
and are called skew lines.
n
line m and line n are
skew lines
m
Throughout this class we will assume that all lines are coplanar
unless otherwise stated.
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When a pair of lines is drawn, two distinct regions are formed:
The interior region lies between the two lines.
The exterior region is the area remaining outside the lines.
A line that intersects two or more lines
in different points is called a transversal.
w
p
Line w intersects line p and line q.
Line w is a transversal.
q
When two lines are intersected by a transversal
four different types of angle pairs are formed.
1 2
3 4
5 6
7 8
Type of angle pair
Definition
Alternate Interior
Angles
Angles are interior angles
Angles are on opposite sides of the transversal
Angles do not have the same vertex
Corresponding Angles
One angle is an interior angle, the other is an exterior angle
Angles are on the same side of the transversal
Angles do not have the same vertex
Alternate Exterior
Angles
Angles are exterior angles
Angles are on the opposite sides of the transversal
Angles do not have the same vertex
Examples
Trick to Identify Angle Pairs: Alternative interior angles form a “Z” shape and corresponding angles form
a “F” shape. You may have to rotate the paper to see the “Z” or the “F”.
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