Question

To prove the triangles are congruent, which of the following rigid motions would map △GHJ to △ZNP ?

(1 point)

Answer 1

To prove that triangles \( \triangle GHJ \) and \( \triangle ZNP \) are congruent using rigid motions, you can use the following steps:

1. **Identify Corresponding Vertices:** First, determine which vertices of \( \triangle GHJ \) correspond to which vertices of \( \triangle ZNP \). For example, if \( G \) corresponds to \( Z \), \( H \) to \( N \), and \( J \) to \( P \), then you can map the triangles accordingly.

2. **Translation:** You might first apply a translation to move one triangle so that one of its vertices aligns with the corresponding vertex of the other triangle. For instance, you could translate \( \triangle GHJ \) so that point \( G \) moves to point \( Z \).

3. **Rotation:** Next, if the triangles are not yet aligned, you may need to rotate \( \triangle GHJ \) around one of its vertices (or around the point that you translated it to) to ensure that the remaining two vertices also align correctly.

4. **Reflection (if necessary):** If the orientation of the triangles does not match after translation and rotation, you may apply a reflection across the line that would bisect the angle formed by the two corresponding vertices.

The specific type of rigid motion (translation, rotation, reflection) needed would depend on the initial positioning and orientation of \( \triangle GHJ \) relative to \( \triangle ZNP \).

If you can provide the exact positioning of points \( G, H, J \) and \( Z, N, P \), I could offer a more tailored answer regarding which motions would be necessary.