Question

wyatt says that both red lines are lines of symmetry. is he correct? why or why not?
options:
no, because neither line goes through a vertex.
yes, because the halves match when the figure is folded along either line.
yes, because both lines go through the center of the figure.
no, because the figure has only one line of symmetry.

Explanation:

Step1: Recall the definition of line of symmetry

A line of symmetry is a line that divides a figure into two congruent (identical) halves such that when the figure is folded along the line, the two halves match exactly.

Step2: Analyze each option

• Option "No, because neither line goes through a vertex": The definition of a line of symmetry does not require the line to pass through a vertex. So this option is incorrect.
• Option "Yes, because the halves match when the figure is folded along either line": If we fold the figure along either of the red lines, the two - halves of the figure will coincide. This satisfies the definition of a line of symmetry.
• Option "Yes, because both lines go through the center of the figure": Just passing through the center is not the criterion for a line of symmetry. For example, a circle has infinitely many lines of symmetry passing through its center, but for an irregular figure, passing through the center is not sufficient. So this option is incorrect.
• Option "No, because the figure has only one line of symmetry": By visual inspection (or the folding test), we can see that there are two lines of symmetry (the red lines). So this option is incorrect.

Answer:

Yes, because the halves match when the figure is folded along either line.