Georgia is justifying the SSS triangle congruence criteria using △ABC and △LMN (image 1). She transforms the first triangle with a translation to create △A′B′C′ (image 2), followed by a rotation to create △A"B"C" (image 3). She is surprised to see that △A"B"C" overlaps △LMN without having done a reflection. What happened? (1 point) Responses Georgia has shown that the two triangles are not congruent. If the sequence of transformations does not include a translation, rotation, and reflection, then the triangles cannot be congruent. Georgia has shown that the two triangles are not congruent. If the sequence of transformations does not include a translation, rotation, and reflection, then the triangles cannot be congruent. Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle. Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle. Georgia made a mistake. She should have done a reflection before the rotation so that her sequence of transformations included all three types of transformations. Georgia made a mistake. She should have done a reflection before the rotation so that her sequence of transformations included all three types of transformations. Georgia made a mistake. She should have translated △ABC along the vector that takes point B to point N , then done a reflection, then done a rotation.

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Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle.

In this case, the translation and rotation that Georgia performed are sufficient to map triangle ABC onto triangle LMN, which demonstrates that the two triangles are congruent without requiring a reflection. The important aspect of triangle congruence is that it can be achieved through various combinations of transformations, and not all three types (translation, rotation, reflection) are necessarily required.

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Georgia is justifying the SSS triangle congruence criteria using △ABC and △LMN (image 1). She transforms the first triangle with a translation to create △A′B′C′ (image 2), followed by a rotation to create △A"B"C" (image 3). She is surprised to see that △A"B"C" overlaps △LMN without having done a reflection. What happened? (1 point) Responses Georgia has shown that the two triangles are not congruent. If the sequence of transformations does not include a translation, rotation, and reflection, then the triangles cannot be congruent. Georgia has shown that the two triangles are not congruent. If the sequence of transformations does not include a translation, rotation, and reflection, then the triangles cannot be congruent. Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle. Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle. Georgia made a mistake. She should have done a reflection before the rotation so that her sequence of transformations included all three types of transformations. Georgia made a mistake. She should have done a reflection before the rotation so that her sequence of transformations included all three types of transformations. Georgia made a mistake. She should have translated △ABC along the vector that takes point B to point N , then done a reflection, then done a rotation.

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Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle.

In this case, the translation and rotation that Georgia performed are sufficient to map triangle ABC onto triangle LMN, which demonstrates that the two triangles are congruent without requiring a reflection. The important aspect of triangle congruence is that it can be achieved through various combinations of transformations, and not all three types (translation, rotation, reflection) are necessarily required.

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GPT-4o mini · Answer

Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle.

In this case, the translation and rotation that Georgia performed are sufficient to map triangle ABC onto triangle LMN, which demonstrates that the two triangles are congruent without requiring a reflection. The important aspect of triangle congruence is that it can be achieved through various combinations of transformations, and not all three types (translation, rotation, reflection) are necessarily required.