Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Triangles

9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Software

Cabri Geometry™
TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 15 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

• ##### Report an Issue

Triangle Proportionality

#### 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