The AAS Congruence Theorem Quick Check 1 of 51 of 5 Items Question Use the image to answer the question. 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 reflection reflection translation translation Skip to navigation page 17 of 17 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

1 answer

To determine which rigid transformation maps triangle \( A"B"C" \) to triangle \( DEF \), we first need to understand the definitions of the transformations involved:

  1. Dilation: A transformation that changes the size of a figure but not its shape.
  2. Rotation: A transformation that turns a figure around a fixed point.
  3. Reflection: A transformation that flips a figure over a line.
  4. Translation: A transformation that slides a figure in a straight line from one position to another.

Since the AAS (Angle-Angle-Side) Congruence Theorem states that if two angles and a non-included side of one triangle are respectively equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent. This means the triangles can be mapped onto each other through one of the rigid transformations listed above, excluding dilation as it changes the size.

Given that you are looking for a rigid transformation:

  • Rotation, reflection, or translation are potential candidates, but the specific answer depends on the arrangement of the triangles.

If the two triangles are suitably oriented without needing to rotate or reflect excessively, a translation may suffice. However, if their positions differ in orientation or mirroring, a reflection or a rotation may be necessary.

Without the specific image or arrangement of triangles provided, it’s not possible to give a definitive answer. Please check the orientation and positioning of triangles \( A"B"C" \) and \( DEF \) relative to each other to select between rotation, reflection, or translation based on their alignment.