Question

a student thinks that the octagon in the diagram to the right has 18 lines of symmetry. explain and correct the students error.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the student counted the total number of arrow heads when they should have just counted the number of lines. therefore, the correct answer is
◯ b. the student counted the total number of lines when they should have just counted the number of arrow heads. therefore, the correct answer is 8
◯ c. the student did not make an error when determining the lines of symmetry.

Explanation:

A line of symmetry is a line that divides a figure into two congruent parts. For a regular octagon, the number of lines of symmetry is equal to the number of sides. A regular octagon has 8 sides, so it has 8 lines of symmetry. The student likely confused the number of arrow - heads (which are just decorative elements in this context) with the number of lines of symmetry. The key is to focus on the geometric property of the octagon (number of sides for a regular polygon gives the number of lines of symmetry).

Answer:

B. The student counted the total number of lines when they should have just counted the number of arrow heads. Therefore, the correct answer is 8.