Question
How can a regular hexagon be folded to show that it has reflectional symmetry?
Fold the hexagon along a line from a vertex to the midpoint of an opposite side.
Fold the hexagon along a line connecting the two midpoints of adjacent sides.
Fold the hexagon along a line that bisects two vertex angles.
Fold the hexagon along a line that creates a right angle at a vertex.
Fold the hexagon along a line from a vertex to the midpoint of an opposite side.
Fold the hexagon along a line connecting the two midpoints of adjacent sides.
Fold the hexagon along a line that bisects two vertex angles.
Fold the hexagon along a line that creates a right angle at a vertex.
Answers
GPT-4o mini
To demonstrate the reflectional symmetry of a regular hexagon, we can use one of the folding methods listed.
A regular hexagon has reflectional symmetry about several axes. One effective way to show this symmetry is by folding the hexagon along a line from a vertex to the midpoint of an opposite side. When you fold the hexagon in this way, the two halves will match perfectly, illustrating that the hexagon is symmetrical about that line.
Here’s a breakdown of each option:
1. **Fold the hexagon along a line from a vertex to the midpoint of an opposite side.**
- This method clearly shows reflectional symmetry, as the vertices opposite to the midpoint will coincide when folded.
2. **Fold the hexagon along a line connecting the two midpoints of adjacent sides.**
- This also demonstrates symmetry since the two halves will align perfectly when folded.
3. **Fold the hexagon along a line that bisects two vertex angles.**
- This method would also illustrate reflectional symmetry of the hexagon, as the angles will match.
4. **Fold the hexagon along a line that creates a right angle at a vertex.**
- This specific folding does not generally yield reflectional symmetry in a regular hexagon.
Thus, several options show symmetry, but folding along a line from a vertex to the midpoint of an opposite side is one clear method to demonstrate the reflectional symmetry of a regular hexagon.
A regular hexagon has reflectional symmetry about several axes. One effective way to show this symmetry is by folding the hexagon along a line from a vertex to the midpoint of an opposite side. When you fold the hexagon in this way, the two halves will match perfectly, illustrating that the hexagon is symmetrical about that line.
Here’s a breakdown of each option:
1. **Fold the hexagon along a line from a vertex to the midpoint of an opposite side.**
- This method clearly shows reflectional symmetry, as the vertices opposite to the midpoint will coincide when folded.
2. **Fold the hexagon along a line connecting the two midpoints of adjacent sides.**
- This also demonstrates symmetry since the two halves will align perfectly when folded.
3. **Fold the hexagon along a line that bisects two vertex angles.**
- This method would also illustrate reflectional symmetry of the hexagon, as the angles will match.
4. **Fold the hexagon along a line that creates a right angle at a vertex.**
- This specific folding does not generally yield reflectional symmetry in a regular hexagon.
Thus, several options show symmetry, but folding along a line from a vertex to the midpoint of an opposite side is one clear method to demonstrate the reflectional symmetry of a regular hexagon.