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Determine if the two triangles are congruent when x=−4. If so, write the congruence statement along with which congruence theorem proves that they are congruent.Two triangles with vertices and sides labeled.(1 point)Responses△QRS≅△TUV by the HL Congruence Theorem. △QRS≅△TUV by the HL Congruence Theorem.△QRS≅△TUV by the SAS Congruence Theorem. △QRS≅△TUV by the SAS Congruence Theorem.The triangles are not congruent.The triangles are not congruent.△QRS≅△TUV by the SSS Congruence Theorem. △QRS≅△TUV by the SSS Congruence Theorem.

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To determine if the two triangles are congruent when \( x = -4 \), we need to analyze the sides and angles of the triangles.

However, I need more specific information regarding the lengths of the sides or angles of triangles \( \triangle QRS \) and \( \triangle TUV \) in order to apply the appropriate congruence theorem (such as SAS, SSS, or HL) to conclude if the triangles are congruent.

  1. If the triangles are right triangles, then we would consider using the HL (Hypotenuse-Leg) Congruence Theorem.
  2. If two sides and the included angle are known, we could use the SAS (Side-Angle-Side) Congruence Theorem.
  3. For three corresponding sides being equal, we would use the SSS (Side-Side-Side) Congruence Theorem.

If you can provide the side lengths or some angles for both triangles, I would be able to help you draw a conclusion about their congruence.

Based on your responses:

  • If you've determined the information already or done the calculations, you can choose the statement that aligns with the congruence theorem you've found applicable to your scenario.

Let me know if you have specific values or any additional details!