# Properties of translations

CCSS Math: 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.

Translate the following line segment by $\langle2,-7\rangle$.
What is the length of the source—the segment before the translation?
What is the length of the image—the segment after the translation?
In order to translate the segment by $\langle 2,-7 \rangle$, we move it two units to the right and seven units down.
By counting the number of units between the endpoints of the line segments, we see that both the source and the image are eight units long.
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.

Translate the following angle by $\langle 5,-6 \rangle$.
Has the measure of the angle changed after the translation?
In order to translate the angle by $\langle 5,-6 \rangle$, we move it five units to the right and six units down.
As the widget shows, the source angle's measure is 45$^\circ$, and the image angle's measure is 45$^\circ$ as well. Therefore, the measure of the angle has not changed.
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.

Translate the following pair of parallel lines by $\langle -4,3 \rangle$.
Are the two image lines parallel?
In order to translate the lines by $\langle -4,3 \rangle$, we move them four units to the left and three units up.