If ΔANT and ΔBRY are similar triangles, the corresponding sides are:
AN ⇔ BR
NT ⇔ RY
AT ⇔ BY
Therefore, in ratio:
AN : BR
NT : RY
AT : BY
Depending on the given measures in the problem, you can solve the measure of the unknown sides in each pair of similar triangles, same with the angles, using the proportion theorem.
You may draw triangles first, if you have doubts, then identify the vertices of each triangle as written.
Example: Δ ABC and Δ DEF are similar triangles.
Do not interchange ABC with ACB, or DEF with FDE.