These are the instructions for students to create the sketch on their own (also available as a Word file):
The purposes of this activity are:
To teach you how to create useful, dynamic sketches in GeoGebra, and use them to explore geometric ideas,
To investigate criteria for proving that triangles are congruent, and
To investigate criteria for constructing triangles given side lengths.
Instructions
Go to geogebra.org and log in (if possible, just link it to your existing google/gmail account to avoid learning yet another username and password!). Create a new Algebra document. Save it as "SSS Triangle Congruence".
Use the Point tool to create a point (A). (A will be the first vertex of our triangle.)
Create three sliders (a, b, and c), with min = 0 and max = 10. (These sliders will represent the lengths of the three sides of our triangle.)
In the input box, type "circle[A, a]" (without the quotes) and hit [return]. This should create a circle centered at point A with radius a. (You can also use the "Circle with Center and Radius" tool to do the same thing.)
Drag the slider for a: you should see the new circle change size as you move the slider.
Create a point (B) on the circle and create line segment (AB) ̅ using the Segment tool. ((AB) ̅ is the first side of our triangle!) GeoGebra will let you move B around the circle, but you can't accidentally drag it off the circle: this means that (AB) ̅ will always have length a, since that's the radius of the circle.
Use the arrow tool to select the circle. You should see that an item in the left panel is highlighted – that's the equation for the circle you clicked. Since we don't need to see the circle anymore, click the blue circle to the left of the highlighted equation. The circle should disappear, but it's still there, just invisible! Check that you can still move B around it, even though you can't see it.
We now need our other two sides, one with length b and one with length c. In the input bar, type "circle[B, b]", then "circle[A, c]". You should now have two circles visible, one with radius b and center B, and one with radius c and center A. Drag the sliders for a, b, and c to make sure they all grow and shrink appropriately. Set the sliders so that a = 2, b = 4, and c = 5.
The two visible circles should intersect in two points. Use the Point tool to create a point (C) at either of the two intersections. Use the Segment tool to connect A to C and B to C. Congratulations! You've created a triangle with the side lengths you specified! (Save your work!)
