Education Technology

Midsegment of a Triangle

Published on 06/09/2008

Activity Overview

Students explore the properties of triangles formed by connecting the midpoints of two sides of a triangle, and examine the relationship between the two triangles. They study the Triangle Midsegment theorem.

Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

  • TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
  • TI-Navigator™  "send to class" feature
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 31 - 35 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Draw a triangle and label its vertices
  • Construct a midsegment by joining the midpoints of two sides of the triangle
  • Check whether the midsegments are parallel to their opposite sides
  • Measure the length of the midsegment and the length of the opposite side of the original triangle
  • Observe that the midsegment is half the length of the opposite side
  • Drag one of the vertices to alter the triangle
  • Verify that for all triangles, a midsegment is parallel to the opposite side and length of the midsegment is half that of the opposite side
  • Find the perimeter and area of the original triangle and the midsegment triangle
  • Alter the triangle and tabulate the perimeter and area of the original triangle and the midsegment triangle
  • Observe that the perimeter of the midsegment triangle is half the original triangle
  • Note that the area of the midsegment triangle is one fourth that of the original triangle
  • Measure the angles of the midsegment triangle and the original triangle
  • Alter the triangle to create an acute triangle, an obtuse triangle, and then a right triangle
  • Notice that the type of triangle formed by the midsegments is the same type of triangle as the original triangle
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary