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

Question

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.

Answer 1

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.