Suppose you are comparing two different triangles to see if they are identical in size and shape. If you check each side and each angle and find they are the same for both triangles, you could conclude that the two triangles are identical. But do you need all six pieces of information to make this conclusion?

1. Open the Congruent Triangles applet.
   
   

   In the triangles below, the red sides and green angles cannot be adjusted. Try moving the black points to see if other triangles can be produced when these lengths and angles are locked. You may need to try all three points in a triangle.

   This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
   
   The applet contains a number of triangles, each with specific constraints. Sometimes side lengths cannot be changed and sometimes angles cannot be changed. Your goal is to determine which set of constraints will guarantee that the triangle is unique. If a triangle cannot be adjusted in any way, the constraints guarantee it is unique.
   
   Complete the following table using the applet.
   
   

   Constraints (parts of the triangle that cannot be changed).	Are triangles with these constraints unique?	If not unique, sketch two different triangles with the same constraints.
   No constraints	No
   1 side	No
   2 sides
   3 sides
   1 angle
   2 angles
   3 angles
   1 side beside an angle
   1 side and 2 angles. The side is not between the two angles.
   1 side and 2 angles. The side is between the two angles.
   2 sides and 1 angle. The angle is between the two sides.
   2 sides and 1 angle. The angle is not between the two sides.

   
   
   
   
2. The table only included up to 3 of 6 possible constraints. Would having 4 or 5 constraints make a triangle unique? Explain your thinking.