### Video Transcript

If π΄π΅πΆπ·πΈπΉ is a regular hexagon whose geometrical center is π, which of the following directed segments are not equivalent? Is it (A) π΅πΆ and π΄π, (B) π΅πΆ and ππ·, (C) π΅πΆ and ππΉ, or (D) π΅πΆ and πΉπΈ?

We will begin by sketching a regular hexagon π΄π΅πΆπ·πΈπΉ. We are told that the geometrical center of the hexagon is π as shown on the diagram. For two directed segments to be equivalent, they need to be of equal magnitude or length and have the same direction. The directed segment π΅πΆ is in all four of our options. There are three other directed segments on the hexagon that are equal to this.

Firstly, we have the directed segment πΉπΈ. π΄π is also equal to both of these as it is of equal magnitude and direction. Finally, we have the directed segment ππ·. As π΅πΆ is equal to π΄π, option (A) is not the correct answer. π΅πΆ is equal to ππ·, so option (B) is not the correct answer. Likewise, π΅πΆ is equal to πΉπΈ, so we can also rule out option (D). The line segment ππΉ, however, is not equal to π΅πΆ. As our hexagon is regular, these segments do have the same magnitude or length. However, they do not act in the same direction.

The correct answer is option (C). The directed segments π΅πΆ and ππΉ are not equivalent. ππΉ would be equivalent to π΅π΄, π·πΈ, and πΆπ. Likewise, the directed segments πΉπ΄, πΈπ, ππ΅, and π·πΆ are equivalent as they have the same length and direction.