**Instructional Implications**Explain to the student the difference between drawing and constructing. Show the student the tools traditionally used in geometric constructions and explain the purpose of each. Be sure the student understands the difference between a ruler and a straightedge.
Guide the student through the steps of the construction (several different methods are described below). Prompt the student to justify each step. Have the student remove any unnecessary marks or marks made in error from his or her paper. Ask the student to write out the steps of the construction and keep them for future reference.
**Method 1:** Locate the point where the perpendicular bisectors of two non-parallel chords meet. Step 1: Use a straight edge to draw two non-parallel chords. Step 2: Construct the perpendicular bisector of each chord. Step 3: Mark the intersection of the perpendicular bisectors to locate the center of the circle.
**Method 2:** Construct a diameter of the circle and bisect it to locate the center. Step 1: Use Method 1 to construct the perpendicular bisector of a chord of the circle. The perpendicular bisector contains a diameter of the circle. Step 2: Construct the perpendicular bisector of the diameter to locate the center.
Allow the student to visualize the construction process. This link provides a step-by-step process for how to find the center of a circle using a compass and straight edge. http://www.mathopenref.com/constcirclecenter.html. Give the student additional opportunities to construct perpendicular lines as part of other constructions such as the construction of a square or rectangle.
Websites such as www.mathopenref.com show the steps of many different constructions. The student is able to watch the construction unfold but can also pause it when necessary.
Have the student construct the center of a circle using paper folding: Step 1: Given a circle on translucent paper, fold the paper so that two halves of the circle coincide. The crease of the fold is a diameter of the circle. Step 2: Repeat the first step to create a second diameter. Step 3: Mark the intersection of the two diameters to locate the center of the circle.
Ask the student to compare the paper folding method to Method 1 above. |