Question

question 10 of 10

if a shape is a regular octagon with eight sides, which of the following must be true?

check all that apply.

a. it has reflectional symmetry.
b. it has exactly one line of symmetry.
c. it has eight lines of symmetry.
d. it is symmetrical.

Explanation:

Analyze regular polygon symmetry

Using the Regular Polygons knowledge point
A regular polygon with \(n\) sides has exactly \(n\) lines of symmetry. For a regular octagon (\(n = 8\)), this means it has exactly eight lines of symmetry.

Evaluate reflectional symmetry

Using the Reflectional Symmetry and Line of Symmetry knowledge points
Since a regular octagon has lines of symmetry, it possesses reflectional symmetry. This also means it is symmetrical.

Assess the given options

Using the Regular Polygons and Reflectional Symmetry knowledge points

• Option A is true because it has reflectional symmetry.
• Option B is false because it has eight lines of symmetry, not exactly one.
• Option C is true because a regular octagon has exactly eight lines of symmetry.
• Option D is true because having lines of symmetry makes the shape symmetrical.

Answer:

• A. It has reflectional symmetry. (Correct answer)
• B. It has exactly one line of symmetry.
• C. It has eight lines of symmetry. (Correct answer)
• D. It is symmetrical. (Correct answer)