Question

select the correct answer.
vincent wants to construct a regular hexagon inscribed in a circle. he draws a circle on a piece of paper. he then folds the paper circle three times to create three folds representing diameters of the circle.
he labels the ends the diameters a, b, c, d, e, and f, and he uses a straightedge to draw the chords that form a hexagon.
which statement is true?
a. vincent’s construction method produces a hexagon that must be regular.
b. vincent’s construction method produces a hexagon that must be equilateral but may not be equiangular.
c. vincent’s construction method produces a hexagon that must be equiangular but may not be equilateral.
d. vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.

Explanation:

Vincent only folds the circle to make three diameters, but there is no requirement that the diameters are spaced at 60° angles (the equal spacing needed for a regular hexagon). If the diameters are not evenly spaced, the chords connecting their endpoints will have different lengths (so not equilateral) and the internal angles of the hexagon will not be equal (so not equiangular).

Answer:

D. Vincent's construction method produces a hexagon that may not be equilateral and may not be equiangular.