Question

Liam and Tehya are trying to determine whether triangle ABC and triangle EFD can be proven congruent through rigid motions.

Liam says that ABC≈EFD because ABC can be reflected over the x-axis to create EFD.
Tehya says that ABC≈EFD because ABC can be rotated 90° clockwise to create DEF.
Who is correct?

Answer 1

The question assesses congruence of triangles ABC and EFD through rigid motions as stated by Liam (reflection over the x-axis) and Tehya (90° clockwise rotation). Both methods can prove congruence if they align all corresponding sides and angles; however, actual congruence depends on the specific details of the triangles' arrangements.

Step-by-step explanation:

The question involves determining whether two triangles, ABC and EFD, can be proven congruent through rigid motions. Applying rigid motions such as reflections or rotations does not alter the size or shape of a geometric figure, which makes them a powerful tool for proving congruence. If Liam's claim that triangle ABC can be reflected over the x-axis to create triangle EFD is correct and Tehya's claim that triangle ABC can be rotated 90° clockwise to create triangle DEF is also correct, then both rigid motions would lead to congruent triangles. However, it is important to verify that these transformations align all corresponding sides and angles appropriately. Thus, without specific coordinates or a diagram, we cannot determine who is correct, but both claims are plausible methods of establishing congruence if the corresponding parts match according to the transformations described.