Unit 13- Geometry as a Mathematical System Flashcards
Theorem
A conjecture that has been proven
Deductive system
A set of premises, or accepted facts, to organize geometry properties
Postulate
A statement that does not need to be proved and is accepted as true
a+b=b+a
Commutative property of addition
ab=ba
Commutative property of multiplication
(a+b)+c=a+(b+c)
Associative property of addition
(ab)c=a(bc)
Associative property of multiplication
a(b+c)=ab+ac
Distributive POE
a=a
Reflexive POE
if a=b and b=c, then a=c
Transitive POE
if a=b, then b=a
Symmetric POE
if a=b, then a+b=c+b
Addition POE
if a=c, then a-b=b-c
Subtraction POE
if a=b, then ac=bc
Multiplication POE
if a^2=b, then a=(plus or minus the square root of b)
Square root POE
If ab=0, then a=0 or b=0 or both equal 0
Zero product POE
congruence
when figures have same size and shape (equal measures)
substitution POE
if a+b=c and b=x, then a+x=c
transitive POE
if a=b and b=c, then a=c
