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If two lines are perpendicular,
then they form congruent, adjacent angles
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If two lines form congruent, adjacent angles,
then the lines are perpendicular
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If the exterior of two acute, adjacent angles are perpendicular,
then the angles are complementary
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If two angles are supplements of congruent angles (or of the same angle),
then the two angles are congruent
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If two angles are complements of congruent angles (or of the same angle),
then the two angles are congruent
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Parallel Lines
coplanar lines that do not intersect
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Skew Lines
noncoplanar lines that are neither intersecting nor parallel
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Parallel Planes
planes that do not intersect
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A line and a plane are parallel...
if they do not intersect
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If two parallel planes are cut by a third plane,
then the lines of intersection are parallel
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Transversal
a line that intersects two or more coplanar lines in different points
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Alternate-Interior Angles
two non-adjacent interior angles on opposite sides of the transversal (always congruent)
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Same-Side Interior Angles
two interior angles on opposite sides of the transversal (always supplementary)
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Corresponding Angles
two angles in corresponding positions relative to the two lines (always congruent)
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If two parallel lines are cut by a transversal,
then corresponding angles are congruent
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If two parallel lines are cut by a transversal,
then alternate-interior angles are congruent
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If two parallel lines are cut by a transversal,
then same side interior angles are supplementary
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If a transversal is perpendicular to one of two parallel lines,
then it is perpendicular to the other one also
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If two lines are cut by a transversal and alternate interior angles are congruent,
then the lines are parallel
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If two lines are cut by a transversal and same-side interior angles are supplementary,
then the lines are parallel
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In a plane, two lines perpendicular to the same line...
are parallel
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Through a point outside a line
there is exactly one line parallel to the given line
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Through a point outside a line,
there is exactly one line perpendicular to the given line
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Two lines parallel to a third line
are parallel to each other
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