Question

which of these triangle pairs can be mapped to each other using a single translation?
image of four triangle diagrams with congruence markings

Explanation:

Step1: Recall Translation Properties

A translation preserves the shape, size, and orientation of a figure. So, the triangle pairs should have the same orientation (same direction of vertices) and congruent corresponding parts.

Step2: Analyze Each Pair

• First pair: Different vertex labels and orientation seems off.
• Second pair (middle graph): Triangles \( \triangle CNE \) and \( \triangle CDE \) (or similar) have same orientation, congruent sides (marked with equal ticks) and right angles, so a translation can map them.
• Third pair: Orientation is rotated, so not a translation.

Answer:

The Middle Graph