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Centers of Triangles

Amy Benson
Mathematics I: Algebra/Geometry/Statistics
Dacula High School
Gwinnett County Schools

Contents

Task
Overview
This task provides a guided discovery and investigation of the points of concurrency in triangles. Students will construct and use the following points:
  • incenter
  • orthocenter
  • circumcenter
  • centroid
In this task students will determine the location for an amusement park by finding the centers of a triangle. The centers will be new to the students but not the constructions. Make sure students remember the significance of points on the perpendicular bisector of a segment (equidistant from the endpoints of the segment) and the points on an angle bisector (equidistant from the sides of the angle).

Learning Task
A developer plans to build an amusement park but wants to locate it within easy access of the three largest towns in the area as shown on the map below. The developer has to decide on the best location and is working with the ABC Construction Company to minimize costs wherever possible. No matter where the amusement park is located, roads will have to be built for access directly to the towns or to the existing highways.

GPS Addressed
MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
    e. Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

Video Information
Use these questions to guide your thinking about some of the important teacher ideas in the lesson featured in the video clip.
  1. What kinds of questions does the teacher ask to promote students’ problem solving?
  2. How is the teacher gauging students’ current understandings and building from those understandings?
  3. Consider the GPS standards listed with this video.
  4. What makes this lesson different from lessons you have taught on this topic?

Classroom Materials

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