Geometry

Question Analysis:
This problem involves overlapping triangles and tests the application of the ASA (Angle-Side-Angle) congruence postulate.

Key Concept Explanation:
The ASA postulate states that two triangles are congruent if they have two corresponding angles and the included side congruent.

Step-by-Step Solution:
Identify the given information:
∠A ≅ ∠C (Given)
AO ≅ CO (Given, marked in the diagram)
∠BOA ≅ ∠DOC (These are vertically opposite angles, which are always congruent.)
Check if the side is included:
AO and CO are the included sides between the congruent angles ∠A and ∠BOA in △AOB, and ∠C and ∠DOC in △COD.
Apply ASA:
Since we have two angles and their included side congruent, we can conclude that △AOB ≅ △COD by ASA.

Option Analysis:
A) Cor...