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