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Question
What theorem proves lines are parallel?
What theorem proves lines are parallel?
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Solution
Parallel lines: The two lines that do not intersect at any point are called parallel lines.
Theorems that prove that lines are parallel:
If a pair of alternate angles formed by a transversal of two lines are congruent then the two lines are parallel.
If two lines in a plane are parallel to a third line in the plane then those two lines are parallel to each other.
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
If two lines are perpendicular to the same line, then they are parallel to each other.
Parallel lines: The two lines that do not intersect at any point are called parallel lines.
Theorems that prove that lines are parallel:
If a pair of alternate angles formed by a transversal of two lines are congruent then the two lines are parallel.
If two lines in a plane are parallel to a third line in the plane then those two lines are parallel to each other.
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
If two lines are perpendicular to the same line, then they are parallel to each other.
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