Geometry

Question Analysis:
This question involves recognizing congruent triangles within a regular hexagon and applying the SAS Congruence Postulate to prove their congruence.
The main focus is on identifying two pairs of corresponding sides and an included angle.

Key Concept Explanation:
A regular hexagon has all sides equal and all internal angles equal (each 120°).
The diagonals of a regular hexagon bisect each other, creating congruent triangle segments.
The SAS Congruence Postulate states that two triangles are congruent if two sides and the included angle are equal.

Step-by-Step Solution:
Verifying the SAS conditions in the answer choices:
Option A (AO ≅ DO, OB ≅ OC, and ∠AOB ≅ ∠DOC) ✅
Two sides are equal (AO ≅ DO and OB ≅ OC).
The included angle ∠AOB ≅ ∠DOC makes it SAS. Correct answer.
Option B (AB ≅ CD, AO ≅ DO, and ∠AOB ≅ ∠DOC) ❌
AB and CD are hexagon sides, but they are not relevant to the SAS condition in △AOB and △DOC.
Option C (AO ≅ DO, AC ≅ BD, and ∠AOB ≅ ∠DOC) ❌
AC ≅ BD refers to entire diagonals, not the i...