Geometry

Question Analysis:
This question involves identifying the congruence of triangles after a rigid transformation — specifically, a translation.
The main focus is on understanding how translations affect the properties of geometric figures.

Key Concept Explanation:
A translation is a type of rigid transformation, meaning it does not change the size or shape of a figure.
It simply shifts the figure a certain distance in a certain direction.
Since rigid motions preserve length and angle measures, translated figures remain congruent to their pre-image.

Step-by-Step Solution:
Determine the type of transformation: The question specifies a translation, which means sliding the triangle without rotating or flipping.
Understand the properties of a translation: Since all side lengths and angles are preserved, the image will be congruent to the original.
Conclude: ΔABC and ΔDEF are congruent due to the rigid transformation.

Option Analysis:
A. Correct – Translations preserve size and shape; this is the definition of congruent figures under rigid motions.
B. Incorrect – While equal angles are a property of congruent triangles, just angles are not sufficient without congruent sides — and this option misses the translation concept.
C. Incorrect – Position does not affect congruence....