Translation of sides, diagonals, etc.

Translating a side, diagonal, or segment in a trapezium means moving it by a fixed vector so that its length and direction stay the same. This is useful for comparing segments, proving parallelism, or constructing congruent segments.

Important properties

• A translation moves every point of a segment the same distance in the same direction.

• Translating a side or diagonal does not change its length or direction.

• If two segments are parallel and equal in length, one can be translated to coincide with the other.

• Translations preserve parallelism and congruence.