| Term | Definition |
|
addition property of equality |
if A=B then A+C=B+C (if AC=DB then AC+CD=DB+CD) |
|
subtraction property of equality |
if A=B then A-C=B-C (if AC=DB then AC-CD=DB-CD) |
|
multiplication property of equality |
if A=B then AC=BC |
|
commutative property of addition |
A+B=B+A |
|
commutative property of multiplication |
AB=BA |
|
associative property of addition |
(A+B)+C=A+(B+C) |
|
associative property of multiplication |
(AB)C=A(BC) |
|
identity property of addition |
A+0=A |
|
identity property of multiplication |
A*1=A |
|
inverse property of addition |
for every "A" there is an (-A) so that A+(-A)=0 |
|
inverse property of multiplication |
A * 1/A= 1 |
|
distributive property |
A(B+C)=AB+AC |
|
reflexive property of equality |
A=A is always true |
|
reflexive property of congruency |
<A~=<A |
|
symmetric property of equality |
if A=B then B=A |
|
symmetric property of congruency |
if <MAD~=<PET then <PET~=<MAD |
|
transitive property of equality |
if A=B and B=C then A=C |
|
transitive property of congruency |
if <AB~=<CD and <CD~=<EF then <AB~=<EF |
|
substitution property |
if A=B then either A or B can be substituted for the other in any other equation |
|
division property of equality |
if A=B then A/C=B/C |
|
segment addition postulate |
if point B lies between point A and C then AB+BC=AC |
|
angle addition postulate |
if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC |