Which sentence explains why polygon ABCDEFGH is congruent to polygon MNOPQRST?

Polygon 1 at: A(6, 6), B(6, 8), C(8, 8), D(8, 4), E(10, 4), F(12, 2), G(4, 2), H(4, 4).

Polygon 2 at: M(12, -6), N(12, -8), O(14, -8), P(14, -4), Q(16, -4), R(18, -2), S(10, -2), T(10, -4).

A. A sequence of translations will map MNOPQRST onto ABCDEFGH.
B. A sequence of rigid transformations will map MNOPQRST onto ABCDEFGH.
C. A sequence of rotations will map MNOPQRST onto ABCDEFGH.
D. A sequence of reflections will map MNOPQRST onto ABCDEFGH.

To map polygon MNOPQRST onto polygon ABCDEFGH, a sequence of rigid transformations, including translations, rotations, and reflections would be used, since they preserve congruence and the polygons are of the same shape and size. The Correct Answer is Option.B.

The question asks which transformations will map polygon ABCDEFGH onto polygon MNOPQRST. To determine this, we can examine the coordinates given for both polygons and look for patterns that indicate a specific type of transformation. By comparing the coordinates for polygons ABCDEFGH and MNOPQRST, we can conclude that a combination of translations, rotations, and reflections can be used to map one polygon onto the other since they have the same shape and size but are in different positions and orientations. Thus, the correct answer is:

B. a sequence of rigid transformations will map MNOPQRST onto ABCDEFGH.

Rigid transformations include translations, rotations, and reflections. These preserve the size and shape of figures, which is necessary for polygons to be congruent. The answer offers a generalized option without specifying one transformation, making it more likely to be correct since more than one type of transformation might be necessary.