2. Constructing Regular Hexagons Inscribed in Circles Adapted from Walch Education

3. Key Concepts Regular hexagons have six equal sides and six angles, each measuring 120˚. The process for inscribing a regular hexagon in a circle is similar to that of inscribing equilateral triangles and squares in a circle. The construction of a regular hexagon is the result of the construction of two equilateral triangles inscribed in a circle. 1.3.3: Constructing Regular Hexagons Inscribed in Circles2

4. 3 Method 1: Constructing a Regular Hexagon Inscribed in a Circle Using a Compass 1.To construct a regular hexagon inscribed in a circle, first mark the location of the center point of the circle. Label the point X. 2.Construct a circle with the sharp point of the compass on the center point. 3.Label a point on the circle point A. 4.Use a straightedge to connect point A and point X. Extend the line through the circle, creating the diameter of the circle. Label the second point of intersection D. (continued)

5. 1.3.3: Constructing Regular Hexagons Inscribed in Circles4 5.Without changing the compass setting, put the sharp point of the compass on A. Draw an arc to intersect the circle at two points. Label the points B and F. 6.Put the sharp point of the compass on D. Without changing the compass setting, draw an arc to intersect the circle at two points. Label the points C and E. 7.Use a straightedge to connect points A and B, B and C, C and D, D and E, E and F, and F and A. Do not erase any of your markings. Hexagon ABCDEF is regular and is inscribed in circle X.

6. Key Concepts Once a circle is constructed, it is possible to divide the circle into six equal parts. Do this by choosing a starting point on the circle and moving the compass around the circle, making marks equal to the length of the radius. Connecting every point of intersection results in a regular hexagon. 1.3.3: Constructing Regular Hexagons Inscribed in Circles5

7. 6 Method 2: Constructing a Regular Hexagon Inscribed in a Circle Using a Compass 1.To construct a regular hexagon inscribed in a circle, first mark the location of the center point of the circle. Label the point X. 2.Construct a circle with the sharp point of the compass on the center point. 3.Label a point on the circle point A. 4.Without changing the compass setting, put the sharp point of the compass on A. Draw an arc to intersect the circle at one point. Label the point of intersection B. (continued)

8. 1.3.3: Constructing Regular Hexagons Inscribed in Circles7 5.Put the sharp point of the compass on point B. Without changing the compass setting, draw an arc to intersect the circle at one point. Label the point of intersection C. 6.Continue around the circle, labeling points D, E, and F. Be sure not to change the compass setting. 7.Use a straightedge to connect points A and B, B and C, C and D, D and E, E and F, and F and A. Do not erase any of your markings. Hexagon ABCDEF is regular and is inscribed in circle X.

9. Thanks for Watching! Ms. dambreville