# Parallel Lines And Transversals

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x = 59, mâˆ 8 = 107Â°
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If mâˆ 3 = (x + 14)Â° and mâˆ 2 = (3x - 70)Â°, What is mâˆ 8?
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x = 14, mâˆ 4 = 34Â°
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If mâˆ 8 = (2x + 6)Â° and mâˆ 2 = (6x - 50)Â°, What is mâˆ 4?
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x = 20, mâˆ 5 = 155Â°
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If mâˆ 7 = (9x - 25)Â° and mâˆ 1 = (4x + 75)Â°, What is mâˆ 5?
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Alternate Interior Angles Theorem
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If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
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corresponding angles
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Angles that lie on the same side of the transversal and in corresponding positions.
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Corresponding Angles Postulate
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If two lines parallel, then corresponding angles are congruent.
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Converse of Corresponding Angles Postulate
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If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.
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alternate exterior angles
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Angles that lie on the same side of the transversal and in corresponding positions.
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Converse of Alternate Exterior Angles Theorem
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If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.
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Alternate Exterior Angles Theorem
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If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
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same side interior angles
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Angles between 2 lines and on the same side of a transversal.
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Same Side Interior Angles Theorem
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If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
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Converse of Same Side Interior Angles Theorem
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If two coplanar lines are cut by a transversal so that a pair of same side interior angles are supplementary, then the two lines are parallel.
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Same Side Interior Angles
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Type of Angles?
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Alternate Interior Angles
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Type of Angles?
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Alternate Exterior Angles
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Type of Angles?
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Corresponding Angles
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Type of Angles?
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perpendicular; midpoint
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The perpendicular bisector of a segment is a line ___ to a segment at the segment's ___.
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perpendicular
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The shortest segment from a point to a line is ___ to the line.
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perpendicular
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âŠ¥ means ___.
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parallel
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|| means ___.
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congruent
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If two intersecting lines form a linear pair of ___ angles, then the lines are perpendicular.
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parallel
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If two coplanar lines are perpendicular to the same line, then the two lines are ___ to each other.
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perpendicular
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In a plane, if a transversal is perpendicular to one of two parallel lines, then it is ___ to the other line.
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Skew
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___ lines are not coplanar. They are not parallel and they do not intersect.
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intersect
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Parallel planes are planes that do not ___.
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Parallel
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___ lines are coplanar and do not intersect.
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skew
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Are the lines parallel, perpendicular, or skew?
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Corresponding Angles
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What type of angle pair are 1 and 5?
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Alternate Interior Angles
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What type of angle pair are 3 and 6?
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Alternate Exterior Angles
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What type of angle pair are 2 and 7?
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Same Side Interior Angles
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What type of angle pair are 4 and 6?
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Linear Pair
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What type of angle pair are 5 and 6?
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Vertical Angles
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What type of angle pair are 6 and 7?
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Perpendicular
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Lines p and q together contain a linear pair in which the angles are congruent. What is the relationship between lines p and q?
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AC
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AF < AB and AF < _____
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supplementary
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When two lines are parallel, the acute angles they form with a transversal are ___ to the obtuse angles.
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Parallel
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Are planes ABF and DHG parallel or perpendicular?
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Perpendicular
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Are planes EFG and BDH parallel or perpendicular?
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Parallel
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Are lines CG and BF parallel or perpendicular?
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Perpendicular
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Are lines GH and FH parallel or perpendicular?
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Line n
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Which line is the transversal?
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3, 6, 7
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Which angles have the same measure as angle 2?
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1, 4, 8
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Which angles have the same measure as angle 5?
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1, 4, 5, 8
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Which angles are supplementary to angle 6?
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2, 3, 6, 7
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Which angles are supplementary to angle 4?
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EFH or HFE
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Angle ABF and angle ___ are corresponding angles.
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Congruent
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Congruent or Supplementary?
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95 degrees
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Find x.
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16
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Find x if f || g.
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x = 77, y = 63
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Solve for x and y.
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None (151 + 28 = 179)
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Which lines, if any, can be proved parallel given the diagram?
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n and p
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If angles 1 and 3 are congruent, which lines must be parallel?
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l and m
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If angles 2 and 5 are congruent, what two lines must be parallel?
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1, 5, 7
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Which angles are on the same side as angle 3?