In this lesson, students build on previous work with perpendicular bisectors and intersections of the medians of triangles to construct the circumscribed circle of a triangle. First, students recall that points on the perpendicular bisector of a segment are equidistant from the vertices of the segment. Then they use this property to conclude that all three perpendicular bisectors of the sides of a triangle intersect at a single point, the triangle’s circumcenter. Students construct the circumcenter and circumscribed circle of a triangle, and conclude that this method would apply to any triangle. Finally, students investigate the locations of circumcenters in right, obtuse, and acute triangles.

One of the activities in this lesson works best when students have access to devices that can run the applet because students will benefit from seeing the relationship in a dynamic way.

Students make use of structure (MP7) as they use the properties of perpendicular bisectors to draw conclusions about triangle circumcenters.