# Department of Mathematics and Computer Science

These following collection of were written with Geometer's Sketchpad®.  If you would like to host the applets locally, please contact Mike May, S.J.

## Applets for Triangles in Geometry

### Triangle Construction

The  Basic Triangle Applet constructs a triangle by dragging the three vertices to the desired locations in the plane.  The length of the sides and the measure of the angles is computed.

The Triangle Side Length Applet lets the user specify the length of the three sides, then constructs the desired triangle.

### Theorem Illustration

The Law of Sines Applet is designed to illustrate the law of sines.  The user drags three points to define a triangle.  The applet computes the length of the three sides and the measure of the three angles.  It then computes the ratio of the length of each side to the values of the sine of the opposite angle.

The Triangle Middle Applet visualizes three theorems in geometry.  For each theorem, you define a method of cutting a triangle in half.  (Use angle bisector, or perpendicular bisector of a side, or line from vertex to midpoint of opposite side.)  Each theorem says the three dividing lines all intersect in a single point.  The applet lets you see this on a triangle that can be distorted and stretched.  It also shows a related construction that is useful in the proof that the three lines connect in a single point.

## Applets for Vectors

### Vectors

The Adding Vectors Applet lets you visualize two vectors with their sum and difference and the vectors measured both in polar and rectangular coordinates.

The Projection, Dot and Cross Product Applet lets you visualize the projection of one vector onto another.  It also gives a visualization of the dot and cross product.

## Applets for Other Courses

The Trig Functions Applet connects the 6 standard trig functions with lengths of line segments from a  diagram connected to the unit circle.

The Reflection Action Applet lets the student explore the action on the standard basis obtained from reflecting across a line through the origin.