Which of these triangle pairs can be mapped to each other using a single reflection?

Question

Triangles F E G and F G L are congruent. Triangle F E G is reflected across line F G to form triangle F G L.
Triangles F E G and G L M are congruent. Triangle E F G is rotated about point G to form triangle G L M.
Triangles F E G and L M N are congruent. Triangle F E G is shifted down and to the right to form triangle L M N.
Triangles L M N and E F G are congruent. Triangle F E G is reflected across a line to form triangle L M N. Triangle L M N is also slightly higher and to the right of triangle E F G.

Answer 1

To determine which triangle pairs can be mapped to each other using a single reflection, we need to analyze the descriptions of the transformations provided for each pair of triangles.

1. Triangles F E G and F G L: Triangle F E G is reflected across line F G to form triangle F G L. This directly states that reflection is used to map these two triangles to each other.

2. Triangles F E G and G L M: Triangle F E G is rotated about point G to form triangle G L M. This means that reflection is not used to map these two triangles.

3. Triangles F E G and L M N: Triangle F E G is shifted down and to the right to form triangle L M N. This indicates a translation, not a reflection.

4. Triangles L M N and E F G: Triangle F E G is reflected across a line to form triangle L M N. However, it's mentioned that triangle L M N is also slightly higher and to the right of triangle E F G, which suggests that it is not a perfect reflection.

From this analysis, only the first pair, Triangles F E G and F G L, can be mapped to each other using a single reflection.