7
QuizMultiple Choice

Construct Regular Polygons

Question 7 • Reading HS- Integrated Math I

Which of the following is true of the constructions of an equilateral triangle, a square, and a regular hexagon when they are inscribed in circles?

Answer
A
The diameter in the first step of the constructions divides each shape in half.
B
Three diameters are needed to construct each inscribed polygon.
C
The arc in step two of each construction divides the circle in half.
D
The line segments that form each shape are congruent to the diameter of the circle.

Explanation

A diameter through the center of a circle can divide each inscribed regular polygon into two matching halves. For an equilateral triangle, it passes through a vertex and the midpoint of the opposite side; for a square and a regular hexagon, it can pass through opposite vertices. The other statements are not true for all three shapes: they do not each need three diameters, and their side lengths are not all equal to the circle’s diameter.

AI-written and checked against the verified answer.

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