Question

1. draw the lines of symmetry for each regular polygon. fill in the table, including an expression for the number of lines of symmetry in an n - sided polygon.

number of sides	number of lines of symmetry
4
5
6
7
8
n

images of a triangle, square, pentagon, hexagon, heptagon, octagon are shown to the right of the table.

Explanation:

Step1: Recall symmetry of regular polygons

A regular polygon with \( n \) sides has \( n \) lines of symmetry, one for each vertex (or side) to the midpoint of the opposite side (or vertex).

Step2: Fill for 3 sides (triangle)

A regular triangle (equilateral) has 3 lines of symmetry.

Step3: Fill for 4 sides (square)

A square has 4 lines of symmetry.

Step4: Fill for 5 sides (pentagon)

A regular pentagon has 5 lines of symmetry.

Step5: Fill for 6 sides (hexagon)

A regular hexagon has 6 lines of symmetry.

Step6: Fill for 7 sides (heptagon)

A regular heptagon has 7 lines of symmetry.

Step7: Fill for 8 sides (octagon)

A regular octagon has 8 lines of symmetry.

Step8: General formula for \( n \) sides

For an \( n \)-sided regular polygon, the number of lines of symmetry is \( n \).

Answer:

Number of Sides	Number of Lines of Symmetry
4	4
5	5
6	6
7	7
8	8
\( n \)	\( n \)