DIRECTIONS TO THE STUDENT:

This diagram is set up so that you can animate either point A or B move a long its dashed line and watch what happens to the measurements of the lengths of the sides of Triangle ABC and also the sums of the lengths of two of the sides. You can move the paths of the points and you can move point C. There will be times when you no longer have a triangle. Can you predict when this will occur? Run the animations in several different arrangements of the diagram and watch what happens to the lengths when this happens. Write a paragraph explaining when and why this occurs. Include in your explanation as many conclusions as you can reach. Think about what stays fixed when something moves and think about whether or not there is ever a greatest or least value for the lengths that are changing.

SCRIPT TO GENERATE THE ANIMATION

Note: This script cannot be re-opened as a Sketchpad Script, you can only follow the steps and record as you go.

Note: Points A and B are the endpoints of one of the dotted segments, Points D and E are the endpoints of the other segment. The fifth point, F, is the stationary vertex of the triangle. The other two triangle vertices are constructed as points on the segments. After the sketch is constructed, the points on the dotted lines and the dotted lines are selected and animation buttons are constructed.

Given:

• Point A
• Point B
• Point D
• Point E
• Point G

Steps:

1. Let [j] = Segment between Point A and Point B.
2. Let [C] = Random point on Segment [j].
3. Let [k] = Segment between Point D and Point E.
4. Let [F] = Random point on Segment [k].
5. Let [l] = Segment between Point G and Point [C].
6. Let [m] = Segment between Point [C] and Point [F].
7. Let [n] = Segment between Point [F] and Point G.
8. Let Measurement [m1] = Length( Segment [l]).
9. Let Measurement [m2] = Length( Segment [m]).
10. Let Measurement [m3] = Length( Segment [n]).
11. Select [C] and [j]. (at this point, animate point C on j and then F on k)