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Parallel Lines
Parallel Lines:( || means parallel)
Parallel lines are lines that do not intersect and are coplanar.
Skew lines:
Skew lines are lines that do not intersect and are not coplanar.
A line and a plane are parallel if they do not intersect.
Theorem:
If two parallel planes are cut by a third plane, then the lines
of
intersection are parallel.
A line that intersects two or more coplanar lines in different
points is called a transversal line.
Consider the figure:
Line t is the transversal of line m and n. The angles that are
produced have special names.
Ð3,4,5,6 are called interior angles. Ð1,2,7,8 are called exterior angles.
The two non adjacent interior angles on opposite sides of the
transversal are called the alternate interior angles.
Ð3 and Ð6
are alternate interior angles.
Ð4 and Ð5
are alternate interior angles.
The two interior angles on the same side of the transversal are
called the same-side interior angles.
Ð3 and Ð5
are same-side interior angles.
Ð4 and Ð6
are same-side interior angles.
The two angles in corresponding positions relative to the two
lines are called the corresponding angles.
Ð1 and Ð5
are corresponding angles.
Ð2 and Ð6
are corresponding angles.
Ð3 and Ð7
are corresponding angles.
Ð4 and Ð8
are corresponding angles.
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