A translation is a geometric transformation that moves all points of a figure the same distance in the same direction. It is often used to map one shape onto another. In this article, we will explore which triangle pairs can be mapped to each other using a single translation.

## Defining Translation

A translation is a transformation in which all points of a figure are moved the same distance in the same direction. The result of a translation is a new figure that is the same shape and size as the original. The magnitude and direction of the translation is described by a vector, which is a line segment with an initial and terminal point.

The vector can be used to identify the direction and magnitude of the translation. For example, a translation of 5 units to the right and 3 units up can be written as a vector (5, 3).

## Triangle Pairs and Mapping

Triangles can be mapped to each other using a single translation if the original triangle and the translated triangle have the same shape and size. For example, if two triangles have the same angles and side lengths, then they can be mapped to each other using a single translation.

However, if the triangles have different angles and side lengths, then they cannot be mapped to each other using a single translation. In this case, a combination of transformations, such as a reflection and a translation, may be necessary in order to map one triangle to the other.

Another way to determine if two triangles can be mapped to each other using a single translation is to check if the corresponding sides and angles of the two triangles are congruent. If the corresponding sides and angles are congruent, then the two triangles can be mapped to each other using a single translation.

In conclusion, triangle pairs can be mapped to each other using a single translation if the original triangle and the translated triangle have the same shape and size. Additionally, two triangles can be mapped to each other using a single translation if the corresponding sides and angles of the two triangles are congruent.