Question

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

Answer 1

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

Explanation:

1. Translation: To map ABCDEFGH onto MNOPQRST, you can imagine moving ABCDEFGH 3 units right and 2 units down so that point G touches point S and point F touches point R.
2. Reflection: Now, you can clearly see they are like opposites, as if there was a mirror. Now you can use reflection over the line y=-2 to map ABCDEFGH onto MNOPQRST

The correct answer is B. To map ABCDEFGH onto MNOPQRST, you need to perform more than one type of rigid transformation (translation and reflection.)
A is incorrect because no matter how you translate it, ABCDEFGH will always be facing up and MNOPQRST will always be facing down, meaning you need more than just translation.
C is incorrect because while you can rotate the shapes onto the same orientation, they will be off because it needs reflection.
D is incorrect because you need translations as well as dilations to map one onto the other.

Hope this helps~