Theorems and Postulates

Addition Property

If a=b then a+c=b+c

Subtraction Propert

If a=b then a-c=b-c

Multiplication Property

If a=b then ac=bc

Division Property

If a=b and c=/ 0 then a/c=b/c

Substitution Property

If a=b then a can be substituted for b in any equation or expression

Reflexive Property

a=a

Symmetric Property

a=b, b=a

Transitive Property

a=b, b=c, then a=c

Proof

A logical argument that shows how a statement is true

2 Column Proof

Has numbered statements in corresponding reasons that show an argument is in logical order

Theorem

A statement that can be proven

Postulate 1

Through any 2 points there’s exactly 1 line

Postulate 2

A line contains atleast 2 point

Postulate 3

If two lines intersect then they intersect at exactly 1 point

Postulate 4

Through any 3 noncolinear points there exists exactly 1 point

Postulate 5

A plane consists of atleast 3 noncolinear points

Postulate 6

If 2 points lie in a same plane then the line containing them lies on the plane

Postulate 7

If 2 planes intersect then their intersection is a line