Question
Which statements are true about the reflectional symmetry of a regular heptagon? Select two options.
It has only 1 line of reflectional symmetry.
A line of symmetry will connect 2 vertices.
A line of symmetry will connect a vertex and a midpoint of an opposite side.
It has 7-fold symmetry.
A line of symmetry will connect the midpoints of 2 opposite sides.
It has only 1 line of reflectional symmetry.
A line of symmetry will connect 2 vertices.
A line of symmetry will connect a vertex and a midpoint of an opposite side.
It has 7-fold symmetry.
A line of symmetry will connect the midpoints of 2 opposite sides.
Answers
GPT-4o mini
For a regular heptagon, the following statements about its reflectional symmetry are true:
1. **A line of symmetry will connect a vertex and a midpoint of an opposite side.** - This is true because it is one of the ways to achieve reflectional symmetry in a heptagon.
2. **It has 7-fold symmetry.** - This statement is also true, as a regular heptagon has 7 lines of symmetry, resulting in 7-fold symmetry.
The other statements are either incorrect or not applicable to a regular heptagon. To summarize, the two correct statements are:
- A line of symmetry will connect a vertex and a midpoint of an opposite side.
- It has 7-fold symmetry.
1. **A line of symmetry will connect a vertex and a midpoint of an opposite side.** - This is true because it is one of the ways to achieve reflectional symmetry in a heptagon.
2. **It has 7-fold symmetry.** - This statement is also true, as a regular heptagon has 7 lines of symmetry, resulting in 7-fold symmetry.
The other statements are either incorrect or not applicable to a regular heptagon. To summarize, the two correct statements are:
- A line of symmetry will connect a vertex and a midpoint of an opposite side.
- It has 7-fold symmetry.