Final answer:
To show similarity between two triangles using angles, the measures of corresponding angles are needed, following the AA (Angle-Angle) similarity postulate.
Step-by-step explanation:
To show the similarity between triangle ABC and triangle A'B'C' using angles, the information needed is the measure of corresponding angles. Triangle similarity can be established under certain conditions, such as AA (Angle-Angle) similarity postulate, where two triangles are similar if they have two corresponding angles that are congruent. In other words, if two angles of one triangle are equal in measure to two angles of another triangle, the triangles are similar. This is because the third angles will also be equal due to the fact that the sum of interior angles in any triangle is always 180 degrees.
When working with similarity, the side lengths of the triangles and the corresponding side ratios are used to show proportional similarity which follows from the angle similarity. However, to establish similarity using angles only, the measures of interior angles are sufficient.