Question

a student thinks that the heptagon in the diagram to the right has 14 lines of symmetry. explain and correct the student’s 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 lines when they should have just counted the number of arrow heads. therefore, the correct answer is

b. the student counted the total number of arrow heads when they should have just counted the number of lines. therefore, the correct answer is

c. the student did not make an error when determining the lines of symmetry.

Explanation:

Step1: Analyze the heptagon's symmetry

A regular heptagon has 7 lines of symmetry. The student likely counted arrowheads (which are 14, as each line has two arrowheads) instead of the lines themselves. So we need to identify the correct reasoning.

Step2: Evaluate the options

• Option A: Talks about counting lines vs arrow heads, but the error is counting arrowheads (total 14) instead of lines. Wait, no—wait, the student said 14 lines, but a heptagon has 7 lines. Wait, maybe the diagram has a regular heptagon (7 -sided), so lines of symmetry equal to number of sides (7). The student counted arrowheads (each line has two, so 7 lines ×2 arrowheads =14). So the student counted arrowheads (total 14) when they should count lines (7). So Option B: "The student counted the total number of arrow heads when they should have just counted the number of lines. Therefore, the correct answer is 7."

Answer:

B. The student counted the total number of arrow heads when they should have just counted the number of lines. Therefore, the correct answer is 7.