Question

Classify the sequences of transformations based on whether or not they prove the congruency of shapes by mapping shape 1 onto shape 2.a. Reflection, Translationb. Rotation, Dilationc. Translation, Rotationd. Dilation, Reflection

Answer 1

Sequences of transformations that preserve the congruency of shapes include Reflection and Translation, as well as Translation and Rotation. Dilation alters the size of a shape, hence sequences including it are not congruency-preserving.

Step-by-step explanation:

To classify the sequences of transformations and determine whether or not they prove the congruency of shapes by mapping shape 1 onto shape 2, we must understand the properties of each transformation:

• Reflection: A flip over a line where the shape's size and shape remain identical, but its orientation changes.
• Translation: Sliding a shape in any direction without altering its size, shape, or orientation.
• Rotation: Turning a shape around a fixed point without changing its size or shape.
• Dilation: A transformation that changes the size of a shape, enlarging or reducing it by a scale factor, but maintains its shape.

Now let's analyze each given sequence:

1. Reflection, Translation: Both transformations preserve size and shape, making shapes congruent.
2. Rotation, Dilation: Rotation preserves congruency, but dilation changes size, which would not prove congruency.
3. Translation, Rotation: Both transformations preserve size and shape, making shapes congruent.
4. Dilation, Reflection: Dilation does not preserve size, though reflection maintains shape, thus this sequence would not prove congruency.