Transitive Property of Congruence

This proof can be demonstrated using any geometric figure. For simplicity, the polygons A, B, and C will be considered.

By definition, two figures are congruent if and only if they have the same size and shape. Also, congruent figures can be placed onto each other by a combination of rigid motions. Since A and B are congruent figures, there is a combination of rigid motions that place A onto B.

In this case, the combination of a rotation and a translation places A onto B. Similarly, since B and C are congruent figures, there is a combination of rigid motions that places B onto C.

The diagram illustrates with a rotation and a translation, B places onto C. Collectively, the rigid motions that place A onto B and B onto C are a combination of rigid motions. Consequently, this combination of rigid motions places A onto C. Therefore, A and C are congruent figures.

The proof is now complete.