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△ABC  and  △DEF  are given in the image. Use the distance formula to determine if  △ABC  is congruent to  △DEF  by the Side-Side-Side Congruency Theorem. Select the four correct statements below.(2 points)ResponsesAB¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯line segment cap A cap b is congruent to line segment cap d cap eAB¯¯¯¯¯¯¯¯≆DE¯¯¯¯¯¯¯¯line segment cap A cap b is not congruent to line segment cap d cap eBC¯¯¯¯¯¯¯¯≅EF¯¯¯¯¯¯¯¯line segment cap b cap c is congruent to line segment cap e cap fBC¯¯¯¯¯¯¯¯≆EF¯¯¯¯¯¯¯¯line segment cap b cap c is not congruent to line segment cap e cap fAC¯¯¯¯¯¯¯¯≅DF¯¯¯¯¯¯¯¯line segment cap A cap c is congruent to line segment cap d cap fAC¯¯¯¯¯¯¯¯≆DF¯¯¯¯¯¯¯¯line segment cap A cap c is not congruent to line segment cap d cap f△ABC≅△DEF△ABC≅△DEF△ABC≆△DEF

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To determine if triangles △ABC and △DEF are congruent using the Side-Side-Side (SSS) Congruence Theorem, you'll need to compare the lengths of the corresponding sides of both triangles. Here are the types of statements you would consider:

  1. Statement about congruent sides: If you calculate the lengths of sides AB, BC, and AC for triangle ABC, and DE, EF, and DF for triangle DEF and find they are equal respectively, then you would have:

    • \(AB \cong DE\)
    • \(BC \cong EF\)
    • \(AC \cong DF\)

  2. Statement about non-congruent sides: If any of the calculated side lengths do not match, you would express:

    • \(AB \ncong DE\)
    • \(BC \ncong EF\)
    • \(AC \ncong DF\)

  3. Statement about triangle congruence: Based on the results of the sides' comparisons, you would conclude either:

    • \(△ABC \cong △DEF\) (if all sides match)
    • \(△ABC \ncong △DEF\) (if any side does not match)

Since I do not have access to the side lengths from the image you referred to, you will need to perform those calculations yourself using the distance formula. The four correct statements will depend on your results from the side lengths.

For example, if your calculations found:

  • \(AB \cong DE\)
  • \(BC \cong EF\)
  • \(AC \cong DF\)

You would select:

  • \(AB \cong DE\)
  • \(BC \cong EF\)
  • \(AC \cong DF\)
  • \(△ABC \cong △DEF\)

On the other hand, if any side lengths were found to be unequal:

  • You would choose the statements reflecting that difference and conclude \(△ABC \ncong △DEF\).

Please do the calculations to determine the correct statements based on the triangle side lengths.