Georgia is justifying the SSS triangle congruence criteria using A ABC and ALMN (image 1). She transforms the first triangle with a translation to create A A'B'C' (image 2), followed by a rotation to create AA" B" C'" (image 3). She is surprised to see that ДА" B" C" overlaps ALMN without having done a reflection. What happened?

Question

Georgia is justifying the SSS triangle congruence criteria using A ABC and ALMN (image 1). She transforms the first triangle with a translation to create A A'B'C' (image 2), followed by a rotation to create AA" B" C'" (image 3). She is surprised to see that ДА" B" C" overlaps ALMN without having done a reflection. What happened?
(1 point)
Georgia made a mistake. She should have translated A ABC along the vector that takes point B to point N, then done a reflection, then done a rotation.
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 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.

GPT-4o mini · Answer

The correct interpretation is: **Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle.** In some cases, two triangles can be congruent through a sequence of transformations that does not require all three types of transformations (translation, rotation, reflection). In this particular scenario, translating and then rotating the first triangle could indeed align it perfectly with the second triangle without the need for an additional reflection. Thus, it is entirely possible for Georgina to demonstrate the congruence of the triangles through those transformations alone.