Question

Which combinations of transformations will always produce congruent figures? Check all that apply.

a dilation, followed by a rotation
a reflection, followed by a dilation
a rotation, followed by a translation
a translation, then a rotation, followed by a stretch
a translation, followed by two reflections

Answer 1

Congruence-preserving (isometric) transformations are translations, rotations, and reflections. Composing any isometries gives an isometry (so congruent figures). Dilations or stretches change size (unless the scale factor is 1), so they do not always give congruent figures.

Thus the combinations that always produce congruent figures are:
- a rotation, followed by a translation
- a translation, followed by two reflections

The others include a dilation or a stretch and so will not always produce congruent figures.