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With the information given in the diagram, which statement is NOT true? The triangles can be proved by the SSS theorem to be congruent. The triangles can be proved by the AAS theorem to be congruent. The triangles can be proved by the ASA theorem to be congruent. The triangles can be proved to be congruent by using rigid motion to match them up exactly

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With the information given in the diagram, which statement is NOT true?
The triangles can be proved by the SSS theorem to be congruent.
The triangles can be proved by the AAS theorem to be congruent.
The triangles can be proved by the ASA theorem to be congruent.
The triangles can be proved to be congruent by using rigid motion to match them up exactly.




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    1 Answer

    1. Quizzma Team

      To determine which statement is NOT true regarding triangle congruence, we need to understand what each theorem signifies:

      1. SSS (Side-Side-Side) Theorem: States that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
      2. AAS (Angle-Angle-Side) Theorem: States that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, the triangles are congruent.
      3. ASA (Angle-Side-Angle) Theorem: States that if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle, the triangles are congruent.
      4. Rigid Motion: This refers to transformations such as translations, rotations, and reflections that maintain the shape and size of the figure.

      If a diagram shows triangles that meet the criteria for SSS, AAS, or ASA, then those statements would be true. If any of these conditions are not met, the corresponding statement would be false.

      Typically, one of these statements may not hold depending on the given conditions in the diagram (e.g., providing only two angles without the necessary corresponding sides could invalidate AAS).

      Without the specific information from the diagram, I suggest reviewing it for side lengths and angle measures to identify which congruence condition is not satisfied.

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