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Properties of Parallel Lines |
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Properties of Parallel Lines:
Postulate:
If two parallel lines are intersected by a transversal, then the
corresponding angles are congruent.
Theorem:
If two parallel lines are intersected by a transversal, then the
alternate interior angles are congruent.
Theorem:
If two parallel lines are intersected by a transversal, then the
same-side interior angles are supplementary.
Theorem:
If the transversal is perpendicular to one of the two parallel
lines, then it is perpendicular to the other one as well.
Postulate:
If two lines are intersected by a transversal and their
corresponding angles are congruent then, the lines are parallel.
Theorem:
If two lines are intersected by a transversal and their alternate
interior angles are congruent then, the lines are parallel.
Theorem:
If two lines are intersected by a transversal and the same-side
interior angles are supplementary then, the lines are parallel.
Theorem:
In a plane, if two lines are perpendicular to the same line then
the lines are parallel.
Theorem:
Through a point not on the line, there is exactly one line
parallel to the given line.
Theorem:
Through a point not on the line, there is exactly on line
perpendicular to the given line.
Theorem:
If two lines are parallel to a third line then they are all
parallell to each other.
Theorem:
If three parallel lines cut congruent segments off a transversal
then, they cut off congruent segments on every transversal.
Corollary:
A line that contains the midpoint of one of the sides of a
triangle and is parallel to another side bisects the third side
of the triangle.
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