Question
Which of these triangle pairs can be mapped to each other using a single reflection?
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.
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.
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GPT-4o mini
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.
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.
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