# Question Video: Identifying Directed Segments of a Geometric Shape Mathematics

If π΄π΅πΆπ·πΈπΉ is a regular hexagon whose geometrical center is π, which of the following directed segments are not equivalent? [A] Line segment π΅πΆ and Line segment π΄π [B] Line segment π΅πΆ and Line segment ππ· [C] Line segment π΅πΆ and Line segment ππΉ [D] Line segment π΅πΆ and Line segment πΉπΈ

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### Video Transcript

If π΄π΅πΆπ·πΈπΉ is a regular hexagon whose geometrical center is π, which of the following directed segments are not equivalent? Is it (A) π΅πΆ and π΄π, (B) π΅πΆ and ππ·, (C) π΅πΆ and ππΉ, or (D) π΅πΆ and πΉπΈ?

We will begin by sketching a regular hexagon π΄π΅πΆπ·πΈπΉ. 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΅πΆ 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 πΉπΈ. π΄π is also equal to both of these as it is of equal magnitude and direction. Finally, we have the directed segment ππ·. As π΅πΆ is equal to π΄π, option (A) is not the correct answer. π΅πΆ is equal to ππ·, so option (B) is not the correct answer. Likewise, π΅πΆ is equal to πΉπΈ, so we can also rule out option (D). The line segment ππΉ, however, is not equal to π΅πΆ. 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΅πΆ and ππΉ are not equivalent. ππΉ would be equivalent to π΅π΄, π·πΈ, and πΆπ. Likewise, the directed segments πΉπ΄, πΈπ, ππ΅, and π·πΆ are equivalent as they have the same length and direction.