Question

1. one definition of similar triangles is based on transformations. however, there are other criteria for determining whether or not triangles are similar. what are these other criteria?

Explanation:

These are standard geometric criteria to verify triangle similarity without relying on transformation definitions, each focusing on side and angle relationships.

Answer:

1. AA (Angle-Angle) Similarity: If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.
2. SAS (Side-Angle-Side) Similarity: If two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent, the triangles are similar.
3. SSS (Side-Side-Side) Similarity: If all three pairs of corresponding sides of two triangles are proportional, the triangles are similar.
4. HL (Hypotenuse-Leg) Similarity (for right triangles): If the hypotenuse and one leg of a right triangle are proportional to the hypotenuse and one leg of another right triangle, the two right triangles are similar.