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Segment addition postulate
AB + BC = AC
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triangle sum theorem
all angles in a triangle add up to 180 degrees
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vertical angle theorem
vertical angles are congruent.
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angle addition postulate
if angle 3 is made of angles 1 and 2, angle 1 plus angle 2 = angle 3
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linear pairs
if 2 angles are linear pairs, they are supplementary
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alternate interior angle theorem
if two parallel lines are cut by a transversal, the pairs of alternat interior angles are congruent.
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alternate exterior angles theorem
if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
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same-side interior angles theorem
if two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary.
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common segments theorem
AB = CD, then AC = BD
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converse corresponding angles postulate
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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purpose of converse of angle theorems:
convert from equal angles to parallel lines
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Perpendicular transversal theorem:
in a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
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dual perpendicular theorem
if two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.
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Right angle congruence theorem
all right angles are congruent
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congruent compliments theorem
if two angles are complementary to the same angle, the two angles are congruent.
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congruent supplements theorem
if two angles are supplementary to the same angle, the two angles are congruent.
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