Question

Use the image to answer the question.



Determine whether triangle DEF
𝐷
𝐸
𝐹
is a translation of triangle ABC
𝐴
𝐵
𝐶
. Enter the number of the correct statement.

Statement #1: Triangle DEF
𝐷
𝐸
𝐹
is a translation of triangle ABC
𝐴
𝐵
𝐶
because each point is translated 8 units to the right and 2 units down.

Statement #2: Triangle DEF
𝐷
𝐸
𝐹
is not a translation of triangle ABC
𝐴
𝐵
𝐶
because the triangles are not congruent.

(1 point)
Statement # is correct.

Answer 1

To determine the correct statement, we need to evaluate the definitions and properties of translations and congruency in triangles.

A translation moves each point of a figure the same distance in a given direction. If triangle DEF is a translation of triangle ABC, then the corresponding points (D to A, E to B, and F to C) must be related by the same translation vector.

Now, let's analyze the two statements:

**Statement #1:** Triangle DEF is a translation of triangle ABC because each point is translated 8 units to the right and 2 units down.
- If this statement accurately describes the movement of triangle ABC to triangle DEF, then it would be a valid statement about translation.

**Statement #2:** Triangle DEF is not a translation of triangle ABC because the triangles are not congruent.
- For triangles to be congruent under a translation, they must have the same shape and size. If triangle DEF is a proper translation of triangle ABC, the two triangles would indeed be congruent.

If triangle DEF can be derived from triangle ABC via a consistent translation vector, then Statement #1 would be the correct one. If they have different shapes or sizes, Statement #2 would be accurate.

Without the actual image to reference, if the description in Statement #1 holds true, then the correct choice would be:

**Statement #1 is correct.**

Conversely, if it has been established that triangle DEF is not congruent to triangle ABC, then:

**Statement #2 is correct.**

Please verify with the visual context or additional details to confirm the outcome.