Question
Which of these triangle pairs can be mapped to each other using a single translation?
Triangles C E D and C N P are congruent. Triangle C E D is rotated about point C and then reflected across a line to form triangle C N P.
Triangles C N E and C E D are congruent. Triangle C N E is reflected across a line and then rotated slightly to form triangle C E D.
Triangles C E D and M D P are congruent. Triangle M D P is rotated and shifted up to form triangle C E D.
Triangles C E D and M P N are congruent. Triangle C E D is shifted to the right to form triangle M P N.
Triangles C E D and C N P are congruent. Triangle C E D is rotated about point C and then reflected across a line to form triangle C N P.
Triangles C N E and C E D are congruent. Triangle C N E is reflected across a line and then rotated slightly to form triangle C E D.
Triangles C E D and M D P are congruent. Triangle M D P is rotated and shifted up to form triangle C E D.
Triangles C E D and M P N are congruent. Triangle C E D is shifted to the right to form triangle M P N.
Answers
GPT-4o mini
To determine which triangle pairs can be mapped to each other using a single translation, we need to understand the transformations applied to each pair of triangles.
1. **Triangles C E D and C N P:** This pair involves rotation and reflection, which means it cannot be mapped using just a translation.
2. **Triangles C N E and C E D:** This pair involves reflection and rotation as well, so it also cannot be mapped using just a translation.
3. **Triangles C E D and M D P:** This pair is described as involving a rotation and then a shift (up). Since it requires a rotation, it cannot be mapped to each other using a single translation.
4. **Triangles C E D and M P N:** This pair indicates that triangle C E D is simply shifted to the right to form triangle M P N. This is a direct translation without any other transformations.
Based on this analysis, the triangle pair that can be mapped to each other using a single translation is **triangles C E D and M P N**.
1. **Triangles C E D and C N P:** This pair involves rotation and reflection, which means it cannot be mapped using just a translation.
2. **Triangles C N E and C E D:** This pair involves reflection and rotation as well, so it also cannot be mapped using just a translation.
3. **Triangles C E D and M D P:** This pair is described as involving a rotation and then a shift (up). Since it requires a rotation, it cannot be mapped to each other using a single translation.
4. **Triangles C E D and M P N:** This pair indicates that triangle C E D is simply shifted to the right to form triangle M P N. This is a direct translation without any other transformations.
Based on this analysis, the triangle pair that can be mapped to each other using a single translation is **triangles C E D and M P N**.