Determine which transformations listed below result in a congruent quadrilateral, A'B'C'D'.

Question

Drag each transformation on the left to indicate whether it is congruent or not congruent to ABCD.

Choices

Rotation followed by dilation
Reflection followed by a translation
Dilation followed by a reflection
Translation followed by a rotation
Answers

Congruent to ABCD
Not Congruent to ABCD

Answer 1

To determine whether the transformations result in a congruent quadrilateral, we need to understand the nature of each transformation:

1. Rotation followed by dilation:

   • Not Congruent to ABCD. Dilation changes the size of the shape, which means the resulting quadrilateral will not be congruent to the original.

2. Reflection followed by a translation:

   • Congruent to ABCD. A reflection and a translation do not change the size or shape of the quadrilateral, so the resulting figure will be congruent to the original.

3. Dilation followed by a reflection:

   • Not Congruent to ABCD. Similar to the first case, dilation will change the size, making the resulting quadrilateral not congruent to the original.

4. Translation followed by a rotation:

   • Congruent to ABCD. Both translation and rotation preserve the size and shape, ensuring the result is congruent to the original quadrilateral.

Summary:

• Congruent to ABCD:

  • Reflection followed by a translation
  • Translation followed by a rotation

• Not Congruent to ABCD:

  • Rotation followed by dilation
  • Dilation followed by a reflection