basic postulates, properties, definitions, and theorems Flashcards
(23 cards)
addition property
if A=B, then A+C=B+C
subtraction property
if A=B, then A-C=B-C
multiplication property
if A=B, then AC=BC
division property
if A=B, then A/C=B/C
reflexive property
any number or value is equal to itself
symmetric property
if A=B, then B=A
transitive property
if A=B and A=C then B=C
substitution property
if A=x, then x can replace A in the problem
distributive property
a(b+c) = ab+ac
definition of perpendicular bisector
if a segment is a perpendicular bisector then it is perpendicular to the line at its midpoint
definition of angle bisector
if a segment is an angle bisector then it cuts the angle in half
definition of complementary angles
if 2 angles add up to 90 degrees then they are complementary angles
definition of supplementary angles
if 2 angles add up to 180 degrees then they are supplementary angles
definition of adjacent angles
if 2 angles are adjacent then they share a vertex and a side
definition of linear pair
if 2 angles are a linear pair then they are both supplementary and adjacent
definition of vertical angles
if 2 angles are vertical then their sides are opposite rays
definition of congruent
if two angles are congruent then they are equal
segment addition postulate
if A, B, and C are colinear and B is between A and C then AB + BC = AC
angle addition postulate
if x is on the interior of angle ACB then the measure of angle ABX + the measure of angle XBC = the measure of angle ABC
vertical angles theorem
if 2 angles are vertical then they are congruent
congruent supplements theorem
if 2 angles are supplements to the same angle then they are congruent
congruent complements theorem
if two angles are complements to the same angle then they are congruent
right angle theorem
if there are 2 right angles then they are congruent
