Question

Use the image to answer the question.

Two triangles, D E F and A double prime B double prime C double prime, are shown.

To show how AAS follows from the definition of congruence, answer the following question. What rigid transformation maps △A"B"C"→△DEF?

(1 point)
Responses

dilation
dilation

rotation
rotation

translation
translation

reflection

Answer 1

To determine how triangle A''B''C'' can be mapped to triangle DEF using rigid transformations, we need to consider the properties of each transformation.

1. **Dilation**: This involves resizing the triangle, which is not a rigid transformation since it changes the size.

2. **Rotation**: This is a rigid transformation that involves turning the triangle around a point, which can potentially map one triangle onto another if they have the same shape and corresponding angles.

3. **Translation**: This transformation involves sliding the triangle to a different position without changing its orientation or size, which does not account for differences in shapes or angles.

4. **Reflection**: This rigid transformation involves flipping the triangle over a line, which can also be used to match corresponding angles and sides.

Given that we want to map △A''B''C'' to △DEF, and since we are looking into AAS (Angle-Angle-Side postulate), it indicates that we are seeking a way to align two triangles based on their angles and one side.

The appropriate response would likely be **reflection**, enabling the triangles to align correctly if they are congruent by AAS congruence criteria.

Thus, the answer is:
**reflection**