Final answer:
In mathematics, to prove the congruence of two triangles, geometric transformations like rotation, reflection, translation, or dilation may be used. Specific methods include congruence postulates such as SSS or SAS, but more detail is needed to determine the exact transformation.
Step-by-step explanation:
To establish the congruence between ΔEBI and ΔBCJ, it is required to apply certain geometric transformations such as rotation, reflection, translation, or dilation. Since the specific question about proving congruence with transformations is not clearly provided, a general method would involve using the Congruent Triangles Postulate or one of its corresponding theorems such as SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), or HL (hypotenuse-leg for right triangles). One would need to demonstrate that all three corresponding sides and angles of the triangles in question are equal. This may involve rotating one triangle to match the orientation of the other, reflecting it over a line, or translating it along a vector. Without additional context or a given figure, it is not possible to determine a specific transformation.