Name. Date. Lesson 2.7 Construct a Regular Octagon A regular octagon has eight equal sides and eight equal angles. Like a square, all of the corners of a regular octagon lie on a circle. Your construction will look like the one to the right. E 1. Construct the perpendicular bisector of AE. (Remember Lesson 2.4?) 2. Label the midpoint of AE, M. 3. Draw a circle with center M and passing through A. 4. Label the points where the circle crosses the perpendicular bisector, C and G. Note: The point M is the vertex of four right angles. One of them has sides MA and MC. In steps 5-7, you will construct the angle bisector of this right angle. 5. Draw a long arc with center A and passing through M. 6. Draw a long arc with center C and passing through M. Be sure that the two arcs cross. (Do you see that this crossing point, and A, M, and C, are corners of a kite?) 7. Draw the angle bisector from M through the intersection of those two arcs. 8. Label the point where the circle with center M intersects the angle bisector, B. 9. Use the method of steps 5-8 to construct the angle bisectors of each of the other three right angles with vertex M. (You will construct a 4-petal flower, too; if you wish, color in the petals with colored pencils!) 10. Label the points where the circle with center M intersects these angle bisectors, D, F, and H. 11. Connect the eight points on the circle to form regular octagon ABCDEFGH. A - E Prufrock Press Inc. . Hands-On Geometry: Constructions With a Straightedge and Compass Permission is granted to photocopy or reproduce this page for single classroom use only. Prufrock Press Inc. Prepared Exclusively for Beth Fawley, 03/04/2011