Which of these Triangle Pairs can be Mapped to Each Other Using a Single Translation?

A. Triangles CNE and CED are congruent. Triangle CNE is reflected across a line and then rotated slightly to form triangle CED.

B. Triangles CED and CNP are congruent. Triangle CED is rotated about point C and then reflected across a line to form triangle CNP.

C. Triangles CED and MPN are congruent. Triangle CED is shifted to the right to form triangle MPN.

D. Triangles CED and MDP are congruent. Triangle MDP is rotated and shifted up to form triangle CED.

Correct Answer: C. Triangles CED and MPN are congruent. Triangle CED is shifted to the right to form triangle MPN.

Explanation:

This option describes triangle CED being “shifted to the right” to form MPN. Shifting is the physical definition of a translation. Because they are congruent and only a shift is required, a single translation suffices.

A translation is a rigid motion that “slides” a figure in a straight line for a certain distance in a specific direction without rotating or flipping it.

Congruence and Orientation: For a single translation to map one triangle to another, they must be congruent and have the same orientation (facing the same direction).

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