Final answer:
To demonstrate congruency between two triangles, the Angle-Side-Angle (ASA) Congruence Postulate could be applied if two angles and the included side are known to be equal for both triangles.
Step-by-step explanation:
To prove that two triangles are congruent, you would apply a congruence postulate. In the scenario described, where the angles and sides are referenced, the postulate that might be used is the Angle-Side-Angle (ASA) Congruence Postulate. This states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. In the example given, the shaded triangles HKD and KFD have a common side KD (or its extension), and they share the 0.5-degree angle at K, and each has a right angle, thus they could be proven congruent by the ASA Congruence Postulate. Similarly, triangles GFC and AHD could also be proven congruent if they have two angles equal to those in HKD and KFD and a side of the same length in the correct position between the angles.