To decide whether two triangles are similar, is it enough to know that one pair of corresponding angle measures is equal?

No, we cannot asses that the two triangles are similar.

Step-by-step explanation:

In order to create similar triangles, dilations must occur with other rigid transformations. These transformations are known as similarity transformations. Dilations preserve lengths, while rigid transformations preserve angles. After dilating, tranforming, and/or translating, the two triangles can map one another.

Being that these two triangles only share one equal angle, they are not similar; no amount of similar transformations can be made to map them onto one another. Their angles and side lengths will simply never fit properly and therefore always prevent similarity.

With only one pair of angles being equal, it is not enough to determine similarity. Thus, two pairs of angles proven equal must be present in order to determine similarity, as it can easily be shown from there that the third pair is equal as well.

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this