Postulates, Proofs, and Theorems

3.1

through any two points, there is exactly one line

3.2

Through any three noncollinear points, there is exactly one plane

3.3

A line contains at least two points

3.4

A plane contains at least three noncollinear points

3.5

If two points lie in a plane, then the entire line containing those points lies in that plane

3.6

if two lines intersect, then their intersection is exactly one point

3.7

If two planes intersect, then their intersection is a line

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

Addition property of equality

if a=b then a-c=b-c

subtraction property of equality

if a=b then ac=bc

multiplication property of equality

if a=b and c≠0 then a/c=b/c

division property of equality

a=a Segments: AB=AB Angles: m<1=m<1

reflexive property of equality

a=b and b=a Segments:AB=CD then CD=AB

symmetric property of equality

if a=b and b=c then a=c Segments: AB=CD and CD=EF then AB=EF Angles: m<1=m<2 and m<2=m<3 the m<1=m<3

Transitive property of equality

if m is midpoint of AB then AM is congruent to MB

midpoint theorem

if a,b and c are collinear then b is between a and c if and only if AB+BC=AC

segment addition postulate

d is in the interior of <ABC if and only if m<ABD + m<DBC= m<ABC

angle addition postulate