b Draw perpendicular segments from each vertex to the line of symmetry.
C
c The hexagon has lines of symmetry that run through both the opposite vertices and the midpoints of opposite sides.
A
aRotated Polygon:
Explanation: See solution.
B
bReflected Polygon:
C
c There are 6 lines of symmetry.
Practice makes perfect
a To rotate the polygon by 180^(∘) we have to use a protractor. We will show how it's done with one vertex.
Place the protractor at the point of rotation, C, and draw two segments. The first segment is drawn from the vertex to the point of rotation. The second segment we draw from the point of rotation and at a 180^(∘) angle with the first segment. Make the segments congruent.
The vertex, marked with a red point, switches positions with its opposite vertex in the hexagon when you rotate it by 180^(∘), and vice versa. We can now draw the rotated hexagon.
b Let's color the top half of the hexagon red, and the lower half blue.
To reflect the hexagon across line n, you have to draw perpendicular segments from each vertex to line n. By extending those segments to the opposite side of n, and with the same length as the first segments, we have reflected all the vertices in n. Let's show this process for each of the halves.
When we reflect the hexagon in line n, the two halves switch sides.
c For a regular hexagon we have 6 lines of symmetry. 3 of them run through opposite vertices in the polygon, and another 3 run through the midpoints of opposite sides.
