Question 1 On a blank sheet of paper, use a compass, a straightedge, and a pencil to construct an equilateral triangle inscribed in a circle. Be sure to leave all compass markings on the paper.

Question

Question 2 Megan thought of another way to construct an equilateral triangle inscribed in a circle. She used her compass, straightedge, and pencil.
Step 1: She used the compass to construct a circle.
Step 2: She used the straightedge to draw a diameter of the circle that extended past the circle.
Step 3: She used her compass, opened to the width of the radius, and put the pointed tip at one of the endpoints of the radius. She constructed a portion of a circle centered at this point.
Step 4: She connected the intersection points of the new circle with the other endpoint of the diameter to make the equilateral triangle.
Compare and contrast the method of constructing an equilateral triangle inscribed in a circle that you used in Question 1 with Megan’s method. How are they similar? How are they different? Which method do you prefer and why?

in 7 sentences and on an 8th grade level

Answer 1

Both methods of constructing an equilateral triangle inscribed in a circle start with drawing a circle, which is the key element in both techniques. In my method from Question 1, I used the circle's center and divided it into three equal parts by marking off points on the circumference. This involves a combination of arcs and angles to ensure all sides are the same length. On the other hand, Megan's method uses a diameter to find points on the circle. She then creates another circle to find the necessary points for the triangle.

The main difference lies in how we find those points: I specifically used angles, while Megan employed another circle based on the radius. I prefer my method because it feels more direct and uses fewer steps, making it easier to visualize the triangle's symmetry. However, both methods effectively achieve the same result, and it's interesting to see different approaches to the same geometric problem.