Determine whether triangle DEF is a translation of triangle ABC . Enter the number of the correct statement.

Question

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

Statement #2: Triangle DEF is not a translation of triangle ABC because the triangles are not congruent.

(1 point)
Statement #
is correct.

Answer 1

To determine which statement is correct regarding whether triangle DEF is a translation of triangle ABC, we need to consider the definitions of translation and congruence.

A translation means that every point in the triangle moves the same distance in the same direction. This means if triangle DEF is indeed a translation of triangle ABC, then all corresponding points (vertices) of triangle DEF should be the same distance from each other as in triangle ABC.

Now, let's analyze the statements:

• Statement #1 states that triangle DEF is a translation of triangle ABC because each point is translated 8 units to the right and 2 units down. If this is true, then triangle DEF would be a translation of triangle ABC as long as the triangles remain congruent.

• Statement #2 claims that triangle DEF is not a translation of triangle ABC because the triangles are not congruent. However, congruence is not a requirement for a translation, as translating a triangle does not change its shape or size. The translated triangle will always be congruent to the original triangle.

Based on this analysis, Statement #1 is correct if it can be established that the points do indeed move exactly as stated. Therefore, the correct answer would be:

Statement #1 is correct.

Answer 2

wrong it was 2

Answer 3

Thank you for your patience, and I appreciate the clarification. Let's break down the reasoning again.

1. Statement #1 claims that triangle DEF is a translation of triangle ABC because each point is translated 8 units to the right and 2 units down. If true, the triangles should be congruent since translations preserve size and shape.

2. Statement #2 states that triangle DEF is not a translation of triangle ABC because the triangles are not congruent.

However, if the triangles are not congruent, it indicates that a translation (which maintains congruence) did not occur. Thus, this statement would indeed be correct if triangle DEF and triangle ABC do not have the same shape and size.

Given your indication that Statement #2 is the correct one, it suggests that the two triangles are not congruent and therefore triangle DEF cannot be a translation of triangle ABC.

So, the correct answer is:

Statement #2 is correct.

Thank you for the correction, and I apologize for the misunderstanding. Please let me know if you have any further questions!