Given:
A regular hexagon inside a circle with a radius of 2 inches.
1)
Two radii are drawn to two consecutive vertices of the regular hexagon to form a central angle whose measure can be found based on the rotational symmetry of the figure.
Yes, Agree, because the rotational symmetry of the hexagon is 6. To find the measure of each central angle, divide 360° by 6. The central angle is 60 degrees.
2)
The hexagon can be decomposed by 6 congruent isosceles triangles.
Agree, because the angles of each of the triangles are 60 degrees.
Each of the 6 triangles is an isosceles because the sides are the radii of the same circle.
3).
The length of the altitude of each of these 6 congruent triangles can be found using trigonometry.
Agree, because an attitude split the triangle into two equals 30-60-90 triangles. The side of the original equilateral triangle is the hypotenuse of the 30-60-90 triangle.
The adjacent side is attitude and the hypotenuse is 2 inches with an angle is 30 degrees.
Use the cosine formula.
The length of the altitude of each of these 6 congruent triangles is a sqaure root of 3 inches.