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x = 59, m∠8 = 107°

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If m∠3 = (x + 14)° and m∠2 = (3x - 70)°, What is m∠8?

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x = 14, m∠4 = 34°

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If m∠8 = (2x + 6)° and m∠2 = (6x - 50)°, What is m∠4?

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x = 20, m∠5 = 155°

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If m∠7 = (9x - 25)° and m∠1 = (4x + 75)°, What is m∠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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⊥ 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?