Question

which diagram represents a line of symmetry for the regular pentagon?

Explanation:

Step1: Define line of symmetry

A line of symmetry divides a shape into two congruent mirror-image halves. For a regular pentagon, this line must pass through a vertex and the midpoint of the opposite side, or through two opposite vertices (but a pentagon has an odd number of vertices, so only vertex-to-opposite-side midpoint lines work).

Step2: Evaluate each option

1. First diagram: The line cuts through two sides, not creating mirror halves.
2. Second diagram: The line passes through a top vertex and the midpoint of the opposite bottom side, splitting the pentagon into two congruent mirror halves.
3. Third diagram: The line cuts through two upper sides, not creating mirror halves.
4. Fourth diagram: The line cuts through the middle of two non-opposite sides, not creating mirror halves.

Answer:

The second diagram (the one with the vertical dashed line passing through the top vertex and the midpoint of the bottom side)