Geometry

Question Analysis:
This question examines the relationship between two triangles whose corresponding sides are in the same ratio (3:4:5).
The key is to determine whether this information alone guarantees congruency, similarity, or other properties.

Key Concept Explanation:
Similar Triangles: Triangles are similar if their corresponding sides are proportional (SSS similarity) and their corresponding angles are equal.
Congruent Triangles: Triangles are congruent if they are similar and the ratio of their corresponding sides is 1:1 (i.e., identical in size).
3:4:5 Triangles: This ratio is characteristic of right triangles (Pythagorean triples), but the actual side lengths can vary (e.g., 3-4-5 and 6-8-10).

Step-by-Step Solution:
Given Information:
The sides of both triangles are in the ratio 3:4:5.
This means the triangles are proportional in shape (SSS similarity).

Evaluate the Options:
A) Congruent: Incorrect. The triangles could be different sizes (e.g., 3-4-5 and 6-8-10).
B) Similar but not necessarily congruent: Correct. The ratio guarantees similarity, but not equal side lengths (congruency).
C) Equal perimet...