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Based on the information marked in the diagram, ΔΔFGH and ΔΔJKL must be congruent.

Question

Based on the information marked in the diagram, ΔΔFGH and ΔΔJKL must be congruent.

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Solution

To determine whether triangles ΔFGH and ΔJKL are congruent based on a given diagram, we would typically follow a structured reasoning process based on the properties of congruent triangles. However, as no specific details or markings from the diagram are provided, here's how to generally approach such a problem:

  1. Identify Given Information: Check the markings or given lengths, angles, and any other relevant information in the diagram that could indicate congruence criteria.

  2. Congruence Criteria: Remember the common criteria for triangle congruence:

    • SSS (Side-Side-Side): All three sides of one triangle are equal to all three sides of another triangle.
    • SAS (Side-Angle-Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
    • ASA (Angle-Side-Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
    • AAS (Angle-Angle-Side): Two angles and a non-included side of one triangle are equal to two angles and the corresponding side of another triangle.
    • HL (Hypotenuse-Leg for right triangles): The hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle.
  3. Apply the Criteria: Based on the information in the diagram, match the criteria.

  4. Conclusion: If any of the congruence criteria are satisfied, then you can conclude that ΔFGH is congruent to ΔJKL (notated as ΔFGH ≅ ΔJKL).

In summary, without seeing the specific diagram and the indicated markings, I cannot provide a detailed answer. However, by following these steps you can analyze the triangles for congruence. Make sure to reference the specific sides and angles indicated in the diagram to apply the appropriate criteria.

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