the intersection of two lines is a point
the intersection of two planes is a line
through any two points there is exactly one line
if two points are in a plane then the line containing them is in the plane
segment congruence postulate
if 2 segments have the same length as measured by a given fair ruler, then the segments are congruent. Also, if two segments are congruent, then they have the same length as measured by a given ruler.
segment addition postulate
if point R is between points P and Q on a line, then PR+RQ=PQ
angle addition postulate
if point S is in the interior of <PQR, then m<PQS+m<SQR=m<PQR
angle congruence postulate
if two angels have the same measure, then they are congruent. if two angles are congruent, then they have the same measure
linear pair property
if two angles form a linear pair, then they are supplementary
If-Then Transitive property
Given:"If A, then B, and if B, then C.: You can conclude "If A, then C"
if a=b, then a+c=b+c
if a=b, then a-c=b-c
if a=b, then ac=bc
if a=b and c does not =0, then a/c=b/c
if a=b, you may replace a with b in any true equation containing a and the resulting equation will still be true.
reflexive property of equality
for any real number a, a=a
symmetric property of equality
for all real numbers a and b, if a=b, then b=a
transitive property of equality
for all real numbers a, b, and c, if a=b and b=c, then a=c.
overlapping angles theorem
given <AOD with points B and C in its interior, the following statements are true: 1. If m<AOB=m<COD, then m<AOC=m<BOD. 2.If m<AOC=m<BOD, then m<AOB=m<COD.
congruent supplements theorem
if two angles are supplements of congruent angles, then the two angles are congruent.