Investigating Mathematics with GeoGebra

Henrico County Public Schools

When can you form a triangle?

READ the instructions on the right and INTERACT with the GeoGebra applet below.
Click on the reset icon icon to reset the diagram.

Sorry, the GeoGebra Applet could not be started. Please install Java 1.4 (or later) to use this page.

Investigation Steps

 Step 1 Close 
  1. Note that AB = 8, AC = 3 and BC = 5 and you have a straight line.

  2. Next, look at the expressions and values on the right. What do you notice? What relationships exist?
 Step 2 Close 
  1. Move points A and B, what changes?

  2. Now, move the AB slider and observe the figures.
 Step 3 Close 
  1. Try moving the other sliders.

  2. Can you describe what happens?
 Step 4 Close 
  1. When is a triangle formed?

  2. What are the values for AB, AC, and BC?
 Step 5 Close 
  1. What are the relationships between the three expressions that must occur to form a triangle?
  2. Formulate the Triangle Inequality Conjecture: The sum of the lengths of any ____ sides of a triangle is _____ the length of the third side.