Short Answer 
To determine if two triangles are similar, first identify corresponding angles, ensuring they are equal using the Angle-Angle (AA) Similarity Theorem. Then, check if the corresponding sides are proportional using the Side-Side-Side (SSS) or Side-Angle-Side (SAS) Similarity Theorem. If both criteria are met, you can conclude that the triangles are similar.
Step 1: Identify Corresponding Angles
Start by examining the two triangles to determine their corresponding angles. For triangles to be similar, all corresponding angles must be equal. This can usually be shown through observation or by using the Angle-Angle (AA) Similarity Theorem. If two angles in one triangle are equal to two angles in another triangle, the triangles are similar.
Step 2: Check for Proportional Sides
Next, analyze the lengths of the sides of the triangles. You need to establish that the corresponding sides of the two triangles are proportional. This means that the ratio of the lengths of one pair of corresponding sides should equal the ratio of the other pairs. You can employ the following similarity theorems based on the available information:
- Side-Side-Side (SSS) Similarity Theorem
- Side-Angle-Side (SAS) Similarity Theorem
- Angle-Angle (AA) Similarity Theorem
Step 3: Conclude About Triangle Similarity
Once you validate the criteria from Steps 1 and 2, you can conclude whether the triangles are similar. If you have established that the corresponding angles are equal and the corresponding sides are proportional, you can confidently state that the triangles are similar. Document your findings, citing the theorems that support your conclusion for clarity.