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Postulates and Theorems

AB
midpointthe point on a line segment that divides it into two equal, or congruent, parts
midpoint
bisectora line or ray that divides an angle into 2 parts
bisector
linear pairtwo adjacent angles that are supplementary
linear pair
perpendicular linesLines are perpendicular when they intersect at a (90degree) (right) angle
perpendicular lines
complementary anglestwo angles whose sum is 90°
complementary angles
supplementary anglestwo angles whose sum is 180 degrees
supplementary angles
congruentidentical in form
congruent
segment addition postulateAB + BC = AC
segment addition postulate
angle addition postulateif two adjacent angles form a larger angle, the sum of the measures of the two smaller angles is equal to the measure of the larger angle
angle addition postulate
substitution propertyif x = y and x = z then y = z
reflexive propertyx = x
symmetric propertyAB = BA
transitive propertyif x = y and y = z then x = z
addition/subtraction/multiplication/division property of equalitywhat you do to one side you do to the other side
right angles congruence theoremall right angles are congruent
right angles congruence theorem
congruent supplements theoremIf two angles are supplementary to the same angle, then they are congruent
congruent supplements theorem
congruent complements theoremif two angles are complements of the same angle, or of congruent angles, then those two angles are congruent
congruent complements theorem
vertical angles conguence theoremwhen two lines intersect, the opposite angles formed (called vertical angles) are always congruent, meaning they have the same measure
vertical angles congruence theorem
linear pair postulateif two angles form a linear pair, they are supplementary



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