Final answer:
The query asks to prove congruency within a geometric scenario that involves intersections of altitudes in a circle-inscribed triangle. Without a clear diagram or additional context, we can only speculate on common geometric properties and theorems that could potentially be used to establish the proof of congruence.
Step-by-step explanation:
The question seems to have components missing, but the typical case of a triangle inscribed in a circle where intersections are considered generally relates to the properties of geometric figures and theorems that explain their relationships, such as congruency and similarity of triangles and the intersection of altitudes known as the orthocenter. Without the full context or a diagram. Nonetheless, the problem appears to contemplate geometric principles which can include the congruence of triangles based on right angles formed at the circle's circumference or other criteria of congruency such as Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Hypotenuse-Leg (HL) for right triangles.
One must consider the various geometric postulates and theorems that are often used to prove congruence such as the triangle congruence criteria. A particular step that may be used in these proofs is the fact that the altitude from the right angle of a right triangle inscribed in a semicircle will be a radius of the circle, leading to congruent triangles based on the Radius Theorem. It is noteworthy, however, that without the specific conditions and the complete setup of the problem, it's speculative to point out the exact method to prove the congruency of triangles. The response provided is plagiarism free as it is based on common geometrical concepts without copying any source.