Geometry Segments Proofs Reference
The midpoint of a segment divides the segment into 2 equal (congruent) parts. If M is the midpoint of AB, then AM=MB.
Definition of Midpoint
Segments are congruent if and only if the have the same measure: If AB is congruent to CD, then AB=CD. If AB=CD, then AB is congruent to CD.
Definition of congruence
EF is congruent to EF
Reflexive property of congruence
For any segment AB, AB is congruent to AB.
Reflexive property of congruence
If AB is congruent to CD, then CD congruent to AB.
Symmetric property of congruence
If AB is congruent to CD and CD is congruent to EF, then AB is congruent to EF.
Transitive Property of congruence
If RS=TU, then RS+XY=TU+XY
addition property of equality
If PQ=PQ, then PQ is congruent to PQ.
definition of congruence
If UV is congruent to UV, then UV=UV
definition of congruence
If LP=PN, and L, P and N are collinear, then P is the midpoint of LN
definition of midpoint
If Y is the midpoint XZ, then XY=YZ
definition of midpoint
If A,B, and C are collinear points and B is between A and C, then AB+BC=AC.
segment addition postulate
If K is between J and L, then JK+KL=JL.
segment addition postulate
If PQ+RS=TV and RS=WX, then PQ+WX=TV
substitution property
If AB+CD=EF+CD, then AB=EF
subtraction property of equality
If CD+DE=CE, then CD=CE-DE
subtraction property of equality
If FG is congruent to HI and HI is congruent to JK, then FG is congruent to JK
transitive property of congruence