Question

Gordon and Tess are trying to determine whether ΔABC and ΔFGE can be proven congruent through rigid motions. Gordon says that ΔABC ≅ ΔFGE because ΔABC can be reflected over the line x = 1 to create ΔFGE. Tess says ΔABC ≅ ΔFGE because ΔABC can be translated by the rule (x + 5, y - 7) to create ΔFGE. Who is correct? A. Gordon only B. Tess only C. Both Gordon and Tess D. Neither Gordon nor Tess

Answer 1

To determine whether ΔABC ≅ ΔFGE is correct through either a reflection or a translation, one must know the vertices' coordinates to validate whether the rigid motions proposed by Gordon and Tess result in congruent triangles. Without specific information about the triangles, we cannot conclusively determine who is correct. It is possible for both claims to be correct if each described motion is a valid transformation that maps ΔABC to ΔFGE.

Step-by-step explanation:

The question at hand is whether ΔABC and ΔFGE can be shown to be congruent through rigid motions. Rigid motions include translations, rotations, and reflections, and they preserve the distance and angle measures of figures. Thus, the congruence of two geometric figures through rigid motions implies that one figure can be moved over the plane without changing its shape or size to exactly cover the other figure.

If Gordon claims that a reflection over the line x = 1 results in ΔFGE from ΔABC, and Tess claims that a translation by the rule (x + 5, y - 7) does the same, we must consider each motion separately. To determine who is correct, assume that the vertices of ΔABC correspond to those of ΔFGE after the stated rigid motions. If the coordinates of ΔABC's vertices perfectly match those of ΔFGE after performing the motion stated by Gordon or Tess, then the corresponding claim is correct. It is possible that both claims are correct if each described motion is a valid transformation for this pair of triangles.

Unfortunately, without knowing the exact coordinates of ΔABC and ΔFGE, we cannot conclude which of the claims is correct. However, keep in mind that it is plausible for both reflections and translations to be valid rigid motions that demonstrate the congruence of two triangles. If both Gordon and Tess have correctly identified a reflection or translation that maps ΔABC to ΔFGE, then both would be correct. Therefore, the correct answer could be C. Both Gordon and Tess, but this is contingent on the specific characteristics of the triangles in question which are not provided here.