# Properties ofÂ translations

CCSS Math: HSG.CO.A.2, HSG.CO.A.4

Learn and verify three important properties of geometrical translations.

When you translate something in geometry, you're simply moving it around. You don't distort it in any way. If you translate a segment, it remains a segment, and its length doesn't change. Similarly, if you translate an angle, the measure of the angle doesn't change.

These properties may seem obvious, but they're important to keep in mind later on when we do proofs. To make sure we understand these properties, let's walk through a few examples.

## Property 1: Line segments are taken to line segments of the same length.

As you can see for yourself, the source and the image are both line segments with the same length. This is true for

*any*line segment that goes under*any*translation.## Property 2: Angles are taken to angles of the same measure.

As you can see for yourself, the source angle and the image angle have the same measure. This is true for

*any*angle that goes under*any*translation.## Property 3: Lines are taken to lines, and parallel lines are taken to parallel lines.

As you can see for yourself, each line is taken to another line, and the image lines remain parallel to each other. This is true for

*any*lineâ€”or linesâ€”that go under*any*translation.## Conclusion

We found that translations have the following three properties:

- line segments are taken to line segments of the same length;
- angles are taken to angles of the same measure; and
- lines are taken to lines and parallel lines are taken to parallel lines.

This makes sense because a translation is simply like taking something and moving it up and down or left and right. You don't change the nature of it, you just change its location.

It's like taking the elevator or going on a moving walkway: you start in one place and end in another, but you are the same as you were before, right?