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26 Cards in this Set
- Front
- Back
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Two coplanar lines that do not intersect.
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parallel lines
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Two non-coplanar lines that do not intersect.
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skew lines
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Two planes that do not intersect.
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parallel planes
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If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
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Postulate 13: Parallel Postulate
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If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
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Postulate 14: Perpendicular Postulate
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A line that intersects two or more coplanar lines at different points.
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transversal
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Two angles that occupy corresponding positions.
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corresponding angles
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Two angles that lie outside the two lines crossed by a transversal, on opposite sides of the transversal.
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alternate exterior angles
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Two angles that lie between the two lines crossed by a transversal, on opposite sides of the transversal.
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alternate interior angles
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Two angles that lie between the two lines crossed by a transversal, on the same side of the transversal.
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consecutive interior angles
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If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
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Theorem 3.1
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If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
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Theorem 3.2
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If two lines are perpendicular, then they intersect to form four right angles.
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Theorem 3.3
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If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
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Postulate 15: Corresponding Angles Postulate
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If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
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Theorem 3.4 : Alternate Interior Angles
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If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary
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Theorem 3.5 : Consecutive Interior Angles
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If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
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Theorem 3.6 : Alternate Exterior Angles
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If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
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Theorem 3.7 : Perpendicular Transversal
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If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
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Postulate 16 : Corresponding Angles Converse
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If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
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Theorem 3.8 : Alternate Interior Angles Converse
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If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
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Theorem 3.9 : Consecutive Interior Angles Converse
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If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
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Theorem 3.10 : Alternate Exterior Angles Converse
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If two lines are parallel to the same line, then they are parallel to each other.
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Theorem 3.11
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In a plane, if two lines are perpendicular to the same line, they they are parallel to each other.
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Theorem 3.12
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In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel.
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Postulate 17 : Slopes of Parallel Lines
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In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.
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Postulate 18 : Slopes of Perpendicular Lines
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