Final answer:
In a regular heptagon, there are 7 lines of reflectional symmetry, each connecting a vertex to the opposite side's midpoint, making statements 1 and 3 true, while statement 4 is incorrect. Statement 2 is correct about rotational symmetry but not reflectional symmetry.
Step-by-step explanation:
The subject of this question is mathematics, and it pertains to the concept of reflectional symmetry in a regular heptagon. A regular heptagon has seven sides of equal length and seven internal angles that are equal. Due to this equality, the heptagon will have lines of symmetry that run from each vertex to the midpoint of the opposite side.
When assessing the statements provided:
It is incorrect to assert that a regular heptagon has 7 lines of symmetry; in fact, a regular heptagon has 7 lines of symmetry, one for each axis that can be drawn connecting a vertex to the midpoint of the opposite side.
It is true that a regular heptagon has 7 rotational symmetries, but this is regarding the ability to rotate the heptagon around its center and have it appear the same.
Since statement 1 is true, statement 3 is essentially the same and therefore also true.
It is incorrect that a regular heptagon has 14 lines of symmetry; this number would be inaccurate for a heptagon.
In conclusion, statement 1 and 3 are accurate in asserting that a regular heptagon has 7 reflectional symmetries, while statement 2 is correct about rotational symmetries but not reflectional symmetries, and statement 4 is incorrect.