Question

6). trapezoid abcd is congruent to trapezoid abcd.
select the 2 ways we could describe the rigid transformations that take abcd onto abcd
a. reflect across line bc
b. rotate 180 degrees counterclockwise around point b, and then translate by directed line segment from b to b
c. rotate 180 degrees clockwise around point c
d. translate by the directed line segment from to c to c, and then rotate 180 degrees around point c
e. translate by the directed line segment from to c to b, and then reflect over line cb

Explanation:

1. Option A: Reflecting trapezoid ABCD across line BC would map it to a shape on the other side of BC, which does not match the orientation and position of A'B'C'D'.
2. Option B: Rotating 180° counterclockwise around point B reverses the trapezoid's orientation, then translating from B to B' moves it to the correct position, resulting in the congruent trapezoid A'B'C'D'.
3. Option C: Rotating 180° clockwise around point C would reorient the trapezoid but place it in a position that does not match A'B'C'D'.
4. Option D: Translating from C to C' moves the trapezoid to the correct general area, then rotating 180° around point C' adjusts the orientation to match A'B'C'D'.
5. Option E: Translating from C to B' and then reflecting over line C'B' would result in a shape that does not match the orientation of A'B'C'D'.

Answer:

B. Rotate 180 degrees counterclockwise around point B, and then translate by directed line segment from B to B'
D. Translate by the directed line segment from to C to C', and then rotate 180 degrees around point C'