Final answer:
The congruency of triangles in the student's question is likely established by the SAS postulate or a similar congruency postulate, highlighting the importance of using mathematical postulates as reliable tools for geometric proofs.
Step-by-step explanation:
The student's question pertains to the identification of the postulate that proves the congruency of triangles. In the context provided, it is likely that the Side-Angle-Side (SAS) postulate is being used to establish the congruency of the shaded triangles HKD and KFD, as they have two sides and the included angle equal. The congruency of the other triangles GFC and AHD to these shaded triangles is likely established by the same or a similar congruence postulate like Angle-Side-Angle (ASA) or Side-Side-Side (SSS), depending on the specific information given.
The Pythagorean Theorem is referenced as a foundational principle, like postulates in trigonometry and physics, which ensures reliability in the results when correctly applied. It highlights the importance of using established postulates and theorems as reliable tools for proving the consistency and congruency of shapes in geometry. This underpins the logical structure of mathematical theory and its practical application in problem-solving.