Triangle CDE and MDP, with shared angles and parallel sides, can be mapped using a single translation, unlike triangle CDE and MNP, which lack complete congruence information.
To determine if two triangles can be mapped to each other using a single translation, we must check if corresponding sides are equal and corresponding angles are congruent. Let's analyze the options:
a. Triangle CDE and MDP: The triangles share a right angle, ED=DP, and CD is parallel to MD. These conditions satisfy the criteria for congruence and can be mapped to each other through translation.
b. Triangle CDE and MNP: Although both triangles have a right angle, ED=PN, and CD is parallel to MN, there is no guarantee that they can be mapped with a single translation. Additional information about the corresponding sides is needed to ensure congruence.
In conclusion, triangle CDE and MDP can be mapped to each other using a single translation, while triangle CDE and MNP lack sufficient information for a conclusive answer.