A translation only changes the position of a figure.
The measures of corresponding angles and the lengths of corresponding sides are equal.
Practice makes perfect
We are told that a triangle L'M'N' is the image of a triangle LMN after a translation. We want to explain how the side lengths and the angle measures of the two triangles are related. Let's consider an example triangle.
We know that a translation only changes the position of a figure, without changing the shape and size. This means that a translation maps angles to angles with the same measure and segments to segments of the same length. Let's consider an example translation. We will translate our triangle 5 units right and 4 units down.
We will compare the side lengths and angle measures of the two triangles. First, we will measure the sides of the two triangles.
As we can see, the sides of △ LMN are the same lengths as the corresponding sides of △ L'M'N'. Now let's measure the angles of the triangles.
The angles of △ LMN have the same measures as the corresponding angles of △ L'M'N'. This confirms that the a translation maps angles of a figure to angles with the same measure and segments of the figure to segments of the same length.
