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