If A, B, and C are collinear, then point B is between A and C if and only if AB+BC=AC
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Reflexive property of congruence
A shape, line, or angle is congruent to itself
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Symmetric property of congruence
Switch sides
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Transitive property of congruence
Has connections
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Angle addition postulate
D is the interior of m∠ABC if and only if m∠ABD + m∠DBC = m∠ABC
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Supplement theorem
If two angles form a linear pair, then they are supplementary angles
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Complement theorem
If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles
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Congruent supplements theorem
Angles supplementary to the same angle or to congruent angles are congruent
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Congruent complements theorem
Angles complementary to the same angle or to congruent angles are congruent
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Corresponding angles postulate
If two parallel lines are cut by a traversal, then each pair of corresponding angles is congruent
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Vertical angles theorem
When two lines intersect, the angles opposite each other are congruent
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Alternate interior angles theorem
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent
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Consecutive interior angles theorem
If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary
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Alternate exterior angles theorem
If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent
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Perpendicular transversal theorem
In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other
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Converse of corresponding angles postulate
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
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Parallel postulate
If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line
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Alternate exterior angles converse
If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel
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Consecutive interior angles converse
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel
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Alternate interior angles converse
If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel
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Perpendicular transversal converse
In a plane, if two lines are perpendicular to the same line, then they are parallel
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Perpendicular postulate
If given a line and a point not on the line, then there exists exactly one line through the point that is perpendicular to the given line
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Corresponding parts of congruent triangles are congruent (CPCTC)
If two triangles are congruent, their corresponding parts are congruent
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Third angles theorem
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent
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Side-Side-Side congruence (SSS)
If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent
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Side-Angle-Side congruence (SAS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent
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Angle-Side-Angle congruence (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
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Angle-Angle-Side congruence (AAS)
If two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent
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Leg-leg congruence (LL)
If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent
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Hypotenuse-angle congruence (HA)
If the hypotenuse and acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent
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Leg-angle congruence (LA)
If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent
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Hypotenuse-leg congruence (HL)
If the hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and corresponding leg of another right triangle, then the triangles are congruent
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Isosceles triangle theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
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Converse of isosceles triangle theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent
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Equilateral triangle
A triangle is equilateral if and only if it is equiangular and each angle of an equilateral triangle measures 60