Geometry

Question Analysis:
This question evaluates the relationship between isosceles triangles with equal base angles, focusing on similarity and congruency.
The key is to recognize that equal angles guarantee similarity, but additional information is needed for congruency.

Key Concept Explanation:
Isosceles Triangle Properties:
Two equal sides (legs) and two equal base angles.
The third angle (vertex angle) is determined by the base angles (since angles sum to 180°).
Similarity: Triangles are similar if their corresponding angles are equal (AA similarity criterion).
Congruency: Requires both equal angles and equal corresponding sides.

Step-by-Step Solution:
Given: Two isosceles triangles with equal base angles.
Their vertex angles must also be equal (since angles sum to 180°).
Thus, all corresponding angles are equal → similarity is guaranteed.

Evaluate Options:
A) Always congruent: False. Similarity does not imply congruency (e.g., a 5-5-6 triangle and a 10-10-12 triangle have equal base angles but different sizes).
B) Equal legs: False. Leg lengths can differ (as in the example above).
C) Equal p...