Reflecting on Transformation of Quadrilaterals

How can we use reflections, rotations, and translations to show that quadrilateral ABCD is congruent to quadrilateral EFGH?

The sequence of transformations to show congruence between quadrilaterals ABCD and EFGH is translation, rotation, and reflection.

To demonstrate that quadrilateral ABCD is congruent to quadrilateral EFGH, we can utilize a sequence of transformations involving translations, rotations, and reflections. These transformations manipulate the position and orientation of the shapes to align them perfectly, proving their congruence.

Explanation:

One possible sequence of transformations to show congruence between quadrilaterals ABCD and EFGH is:

  1. Translation: Slide quadrilateral ABCD so that vertex A coincides with vertex E.
  2. Rotation: Rotate quadrilateral ABCD by 180 degrees so that side AB coincides with side EF.
  3. Reflection: Reflect quadrilateral ABCD across the line of symmetry that runs through the midpoints of sides AB and EF.

After these transformations, quadrilateral ABCD will be congruent to quadrilateral EFGH, showcasing the relationship between the two shapes through the manipulation of their positions and orientations.

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