Reflection Symmetry

Reflectional Symmetry Example

Use the interactive applet below to explore the lines of symmetry of the 14 figures.

Symmetry Practice

For each figure determine the number of lines of symmetry, degrees of rotational symmetry and the order of the polygon.

Question 1

How many lines of reflection does the regular (equilateral) triangle have?

Question 2

How many lines of reflection does the square have?

Question 3

How many lines of reflection does the regular pentagon have?

Question 4

How many lines of reflection does the regular hexagon have?

Question 5

How many lines of reflection does the regular heptagon have?

Question 6

How many lines of reflection does the regular octagon have?

Question 7

What connection can you make about the lines of reflection and vertices of a regular polygon?

Question 8.

How many lines of reflection would an isosceles triangle have? Hint: use the folding applet at the beginning of this activity to assist in finding the lines of reflections (figure 2 is an isosceles triangle).

Question 9.

How many lines of reflection would an isosceles trapezoid have? Hint: use the folding applet at the beginning of this activity to assist in finding the lines of reflections (figure 8 is an isosceles trapezoid).

Question 9

How many lines of reflection does the rectangle have? How is the rectangle different from the isosceles triangle and trapezoid in terms of congruent sides?

Question 10.

How many lines of reflection does the parallelogram have? Hint: See Figure 8 in the applet above.

Question 11

How many lines of reflection does the rhombus have? Hint: See Figure 5 in the applet above.

Question 12.

The rhombus is a special type of parallelogram because each side is congruent; in this way, it is similar to a square. Explain why the rhombus has fewer lines of reflection than the square and more lines of reflection than the parallelogram.