Geometry

Question Analysis:
This question tests understanding of valid triangle congruency postulates and theorems.
The main focus is on distinguishing between methods that prove congruency versus those that only prove similarity.

Key Concept Explanation:
Valid congruency methods (SSS, SAS, ASA, AAS, HL) require a combination of equal sides and angles that uniquely determine a triangle's size and shape.
AAA (Angle-Angle-Angle) only ensures triangles have the same shape (similarity) but not necessarily the same size.

Step-by-Step Solution:
Evaluate each option:
A) SSS: Valid. Three equal corresponding sides force congruency.
B) SAS: Valid. Two sides and their included angle uniquely determine a triangle.
C) AAA: Invalid for congruency. Triangles can have identical angles but different sizes (e.g., a triangle and its scaled-up version).
D) ASA: Valid. Two angles and their included side uniquely determine a triangle.
Why AAA fails for congruency:
Example: A 30°-...