Question

Instruction: Match the provided statements to their corresponding reasons, or vice-versa.

During a rainy day, a student observes that the shape of an umbrella, whether fully opened or partially closed, forms various triangular patterns. The ribs of the umbrella, connected to the central shaft, are evenly distributed and support the fabric to maintain its shape. The student notices that the triangular spaces formed by the shaft and the ribs appear to be congruent.

Given: Quadrilateral RAIN is a parallelogram, and $\overline{\mathrm{AN}}$ is a diagonal.

Prove: $\Delta ARN\cong\Delta NIA$

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