Question

Which sentence best explains why shape 1 and shape 2 are not congruent?

1) Shape 1 cannot be mapped onto shape 2 using a dilation.
2) Not all corresponding pairs of sides on the two shapes are perpendicular.
3) Shape 1 cannot be mapped onto shape 2 using a reflection.
4) Not all corresponding pairs of sides on the two shapes are parallel.
5) There is no sequence of rigid transformations that will map shape 1 onto shape 2.

Answer 1

The sentence that best explains why shape 1 and shape 2 are not congruent is:

therefore correct option is (5).

5) There is no sequence of rigid transformations that will map shape 1 onto shape 2.

Congruent shapes must be the same size and shape, which means one shape can be mapped onto the other using rigid transformations, which include rotations, reflections, and translations (and not dilations, as they can change the size of the shape). If shape 1 cannot be mapped onto shape 2 using any sequence of these rigid transformations, then they are not congruent.

The other statements involve conditions that are either not sufficient to prove non-congruence (such as the perpendicularity or parallelism of corresponding sides) or include a non-rigid transformation (dilation), which is not used when determining congruence.

Answer 2

Shape 1 and shape 2 are not congruent because there is no sequence of rigid transformations that will map shape 1 onto shape 2, as stated in option 5.

Step-by-step explanation:

The sentence that best explains why shape 1 and shape 2 are not congruent is option 5: There is no sequence of rigid transformations that will map shape 1 onto shape 2. Congruent shapes are those that can be mapped onto each other using rigid transformations, which include rotations, reflections, and translations.

If a shape does not match another using any combination of these transformations, they are not congruent. The other options mention conditions that are not definitive factors in determining congruence.

For instance, non-perpendicular or non-parallel sides do not necessarily prevent two shapes from being congruent, and the mention of a dilation is irrelevant since dilations are not considered rigid transformations because they change the size of the shape.