Education Technology

Triangle Proportionality

Published on 06/09/2008

Activity Overview

In this activity, students will study the concept of triangle proportionality.

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 61 - 64 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Construct a triangle XYZ
  • Draw a line parallel to XZ which intersects side XY in point A and side YZ in point B
  • Measure XA, YA, ZB, and BY
  • Calculate the ratios XA / AY and ZB / BY
  • Observe that the ratios are same
  • Alter the triangle to check the relationship
  • Note that the ratios stay equal if the triangle is changed, but differ when the parallel line is relocated
  • Observe that a line parallel to one side of a triangle intersects the other two sides and divides the two sides proportionally

  • Construct a triangle ABC
  • Bisect angle ABC
  • Label the point of intersection of the angle bisector and side AC as Z
  • Measure AZ, ZC, AB, and BC
  • Calculate the ratios AZ / ZC and AB / BC
  • Observe that the ratios are equal
  • Observe that a line that bisects an angle of a triangle divides the opposite side into segments, which are proportional to the lengths of the other two sides
  • After the Activity

    Review student results:

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