The correspondence between the two shapes' angles and sides proved they were congruent.
The rotation and reflection involved in the transformation established a one-to-one correspondence between the preimage and image.
The line of symmetry divided the figure into two halves with perfect correspondence.
Each point on one side of the circle corresponds to exactly one point on the other side, due to the circle's line of correspondence.
By establishing the correspondence between the shapes' vertices, the geometer proved they were similar.

Communication by the exchange of letters.

Nouns denoting communicative processes and contents.

Compatibility of observations; "there was no agreement between theory and measurement"; "the results of two tests were in correspondence".

Nouns denoting attributes of people and objects.

The researchers found a strong correspondence between the predicted outcomes and the actual experimental results.
The data from the two studies were in perfect correspondence, confirming the initial hypothesis.
There was a lack of correspondence between the theoretical models and the observational evidence.
The team noticed a high degree of correspondence between the simulated and actual behavior of the complex system.
A thorough analysis revealed a striking correspondence between the patterns observed in the natural environment and those predicted by the mathematical model.