Investigating Mathematics with GeoGebra

Henrico County Public Schools

What do these three triangles have in common, besides a side of seven?

READ the instructions on the right and INTERACT with the GeoGebra applet below.

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

Based on a problem by Jim Loy.

Investigation Steps

Click on the reset icon icon to reset the diagram.

 Step 1 Close 
  1. At first the question seems a little difficult to answer but let´s determine where they are different.

  2. Are ΔABC, ΔDEF and ΔGHK the same type?

  3. Are the triangles perimeters the same?
 Step 2 Close 
  1. Each has the same base, are their heights the same?

  2. What can you say about their the area of each triangle?

  3. So, what must be the same in each triangle?
 Step 3 Close 
  1. That´s it, they must have an angle that has the same measure, but which one and what is its measure?

  2. Use the angle icon tool to measure the angles in each triangle.

  3. What angles are the same? Where are they located in the triangle?