Use the image to answer the question.

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