Once a triangle is proven congruent, then we can make the conclusion that all parts, including corresponding sides and angles, are congruent.

That is correct. When two triangles are proven congruent using any of the congruence postulates or theorems, such as Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA), we can conclude that all corresponding sides and angles of the triangles are congruent. This is because congruence between triangles means that they have the same shape and size, so all corresponding parts will be equal.