Lesson 2: Writing scripts

Basics

In these exercises you will learn how to record constructions as Sketchpad scripts so that the sequence of operations can be saved and repeated. This will make further constructions much faster and will provide a greater incentive for carrying out complicated constructions.
You will find that you may have to try recording a construction several times before you get it to perform just the way you want it to. This seems a bit frustrating at first, but it will be worth it in the end.
Be sure to test out your scripts after you have saved them. Don't be afraid to scrap them and start over until you get them right!

Exercises

Complete, test, and save scripts for each of the following constructions.

1. Construct an equilateral triangle based on two points. These two points will form two of the vertices. As you test, make sure you know how to select the points so that your triangle is drawn where you want it to be.
2. Construct the "midpoint" or medial triangle, whose vertices are the midpoints of the three edges of a triangle, based on the three edges.
3. Construct the unique circle going through three points, based on the three points.
4. Construct the inscribed circle of a triangle based on the three vertices.
5. Construct an escribed circle for a triangle based on the three vertices. The order in which you select the vertices when you run the script will determine which escribed circle is drawn. Recall that the escribed circle is the intersection of the perpendiculars to two of the angle bisectors.
6. Construct the centroid of a triangle based on the three vertices.
7. Construct the quadrilateral formed by the perpendicular bisectors of a given quadrilateral, based on the four edges of the quadrilateral, selected in some particular order.
8. Construct the pedal triangle for a triangle based on the three vertices of the triangle and the pedal point. Make sure that you always get a triangle. even if some of the vertices lie outside the original triangle.
9. Construct the tangent lines to a circle from a point outside the circle, based on the outside point, the center and the circle

Investigations

1. Open a new sketch.
   • Construct a triangle ABC, a point P, not on any of the sides of ABC, and the pedal triangle, A'B'C', to ABC from P. Use your script!!
   • Drag P around the sketch and observe the changes in the shape of the pedal triangle. Is there a position for P where A'B'C' deteriorates into a line segment? Is there more than one such location? Can you identify the locus of all such points? Can you check your conjecture?
   • Construct the pedal triangle A''B''C'', to A'B'C' from the same point P. Repeat this to get the pedal triangle A'''B'''C''' to A''B''C'' from P. What is the relationship between ABC and A'''B'''C'''? Does it always hold? How would you check that your conjecture is correct?
   Write your conclusions in a text box on the sketch.
2. Open a new sketch and construct a triangle ABC.
   • Use your script to construct an equilateral triangle pointing out from each edge. Then use another script to construct the centroid of each of these three new triangles.
   What kind of a triangle is formed by these three new point? Join each of the original vertices to the opposite new center and what do you find? Join each of the original vertices to the opposite vertex of a new triangle and what do you find? This is an amazingly rich figure. Make as many observations about it as you can. Write your conclusions in a text box on the sketch.
3. Open a new sketch. Construct a quadrilateral ABCD.
   • Use your script to construct the quadrilateral EFGH formed by the perpendicular bisectors of the edges of ABCD. Can you move the vertices of the original quadrilateral so that the new quadrilateral deteriorates to a line segment or to a point? Is there more than one way to do this? Can you describe the circumstances that produce this? Can you check your conjecture?
   • Use your script again to construct the quadrilateral IJKL from the perpendicular bisectors of ABCD. How is this quadrilateral related to the original one? How would you verify your conjecture?
4. Open a new sketch. Construct a triangle ABC.
   • Use your scripts to construct the three escribed circles and the inscribed circle.
   Find as many interesting facts as you can about this figure. Write your conclusions in a text box on the sketch.

Homework

Hand in electronic copies of your completed investigations. Make sure your name is on each individual sketch.