Which sentence best explains why shape 1 and shape 2 are not congruent?
a.
shape 1 cannot be mapped onto shape 2 using a reflection.
b.
shape 1 cannot be mapped onto shape 2 using a dilation.
c.
there is no sequence of rigid transformations that will map shape 1 onto shape 2.
d.
not all corresponding pairs of sides on the two shapes are parallel.
e.
not all corresponding pairs of sides on the two shapes are perpendicular.

The correct option is C:

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

Step-by-step explanation:

Shape 1 has 7 sides thus it is a heptagon.

Shape 2 has 8 sides thus it is a octagon.

In transformations like translation, rotation, dilation, the shape of the final image remains same, only the orientation and size changes.

In the given picture shape 1 is heptagon and shape 2 is octagon.

It does not matter whether the sides of the shapes are parallel or not

Therefore in no way any transformation can yield shape 2 from shape 1.

Thus the correct option is C...

a

b

d

step-by-step explanation: