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B) The completed construction of a regular hexagon is shown below. Explain why AACF is a 30°-

60°-90° triangle. (10 points)

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ACF is a 30º-60º-90º triangle because of the following:

1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 :
√(3)

1 → short leg

2 → hypotenuse


√(3) → long leg

Side length of the hexagon is the short leg of the triangle. It is 1.

r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.

Using Pythagorean theorem.


a^2 + b^2 = c^2


1^2 + b^2 = 2^2


b^2 = 2^2 - 1^2


b^2 = 4 - 1


b^2 = 3


√(b^2) = √(3)


b = √(3)

B) The completed construction of a regular hexagon is shown below. Explain why AACF-example-1
B) The completed construction of a regular hexagon is shown below. Explain why AACF-example-2
B) The completed construction of a regular hexagon is shown below. Explain why AACF-example-3
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