There are a number of different ways that the JSP Constructor can be used in educational activities. It can be used to construct geometric objects, to complete the construction of geometric objects, or to construct an applet. Each of these activities can be used to do things like demonstrating a geometric proof.
Some example activities are provided below. Each activity should have complete instructions, and if necessary a zip file containing the partially completed construction. This file should be placed in the main directory from which the JSP Constructor is run. It can then be loaded by the JSP Constructor, and completed.
INCENTRES
Start with a triangle, two of its angle bisectors and their point of intersection.
First activity
Construct the third angle bisector. Note that it
passes through the intersection point of the first two.
Drag the vertices of the triangle around to convince yourself that
this is true for triangles of any shape. The point
where the three angle bisectors of a triangle meet is called the incentre
of the triangle.
Second activity
The incentre has the interesting property that it
is the same distance from each of the three
sides of the triangle. Check this out: for each side of the triangle,
construct the line through the incentre and
prependicular to that side, and construct the point where this perpendicular
line intersects the side. Measure the
distance from each of these constructed points to the incentre and
notice that all three are equal. Drag the vertices
of the triangle around to check that this is always true. This number
is called the inradius of the triangle.
Third activity
Construct the circle whose centre is the incentre
of the triangle and whose radius is its inradius.
This circle passes through each of the three points constructed in
the last activity. It is also tangent to each of the
three sides of the triangle (drag to check that this is always true).
This circle is called (suprise) the incircle of the
triangle.
PAPPUS' THEOREM. Start with two lines and three points on each:
points A1, B1, C1 on one and A2, B2, C2
on the other.
Activity
Construct:
* lines A1-B2, B1-A2 and their point of intersection
* lines B1-C2, C1-B2 and their point of intersection
* lines C1-A2, A1-C2 and their point of intersection
What do you notice about the three new points? Construct
a line through two of the new points and use it to see if
your guess is correct for this pair of starting lines. Then drag the
starting lines around to check if your guess is true
for all pairs of starting liines..