Final answer:
The correct rule of congruence for ∆KAP being congruent to ∆AKR cannot be determined without additional information about the triangles' sides or angles. The congruence postulates SAS, ASA, SSS, and AAS require specific details to identify the correct rule.
Step-by-step explanation:
To determine by what rule ∆KAP is congruent to ∆AKR, we would need information about the sides or angles in the triangles. The congruence postulates mentioned in the question are Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Side-Side-Side (SSS), and Angle-Angle-Side (AAS). Without specific details on how the triangles relate to each other, it's not possible to determine the correct rule of congruence. Thus, in this scenario, the necessary information to answer the question is missing, and an accurate response cannot be provided. In general, SAS states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. SSS states that if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. Lastly, AAS states that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, the triangles are congruent