Question

3. ABCD is a rectangle. Trapezoid AEFB is congruent to trapezoid CFED. G is the midpoint of segment E F

D
E
B
C
Select all the ways we could describe the rigid transformation that takes AEFB to CFED.
a. Reflect AEFB across line EF.
b. Rotate AEFB 180 degrees counterclockwise around point G.
c. Rotate AEFB 180 degrees clockwise around point G.
d. Translate AEFB by the directed line segment from F to E, and then reflect across line FF
e. Translate AEFB by the directed line segment from F to E, and then rotate 180 degrees clockwise around point E.

Answer 1

The rigid transformation that takes AEFB to CFED can be described as a reflection across line EF, or a rotation of 180 degrees counterclockwise or clockwise around point G1.

Since trapezoid AEFB is congruent to trapezoid CFED, we can transform AEFB onto CFED using a rigid transformation. Since G is the midpoint of segment E F D E B C, it is the center of rotation or the point of reflection.

Option a is correct because reflecting AEFB across line EF will result in CFED.

Option b is correct because rotating AEFB 180 degrees counterclockwise around point G will result in CFED.

Option c is correct because rotating AEFB 180 degrees clockwise around point G will also result in CFED.

Option d is incorrect because translating AEFB by the directed line segment from F to E and then reflecting across line FF will not result in CFED.

Option e is incorrect because translating AEFB by the directed line segment from F to E and then rotating 180 degrees clockwise around point E will not result in CFED.

Therefore, the correct options are a, b, and c.