Dynamic Geometry

Dynamic geometry software allows for traditional constructions with compass and straightedge to be performed by computer and to then be manipulated in a dynamic way.

This page shows a few examples using Geometer's SketchPad and Cabri Geometry II. At present, they are simple examples to illustrate how the software works. In this case, a Java version of GSP (Java SketchPad) and of Cabri (CabriJava) are used to construct objects which can be manipulated by the user.

The Circle example allows a user to manipulate a circle by dragging either the centre or a point on the circumference. As these are dragged, the circle changes size, and the radius, perimeter and area are recorded automatically. The ratios of circumference to radius and area to squared radius remain constant, however. Try the Circle applet for yourself.

The Medians of a triangle are constructed and seem to be concurrent. As you move the vertices of the triangle around, the medians are correspondingly changed, but they still appear to be concurrent, suggesting that this is a general property of medians. Try the Medians applet for yourself.

The Altitudes of a triangle are constructed and seem to be concurrent. As you move the vertices of the triangle around, the altitudes (or perpendicular heights) are correspondingly changed, but they still appear to be concurrent, suggesting that this is a general property of altitudes. Try the Altitudes applet for yourself.

The Perpendicular bisectors of the sides of a triangle are constructed and seem to be concurrent. As you move a vertex of the triangle around, two perpendicular bisectors are correspondingly changed, while the third is not changed. The three perpendicular bisectors still appear to be concurrent, suggesting that this is a general property of triangles. Try the Perpendicular bisectors applet for yourself.

The CabriJava version of the Perpendicular bisectors applet shows how the perpendicular bisectors of the sides of a triangle are concurrent. As you move the vertices of the triangle around, two perpendicular bisectors are correspondingly changed, but the three bisectors still appear to be concurrent, suggesting that this is a general property of triangles. Try the Perpendicular Bisectors applet using CabriJava for yourself. [Seems not to be working yet ... still in progress!]

A pair of lines intersects at a point, and the Angles formed by the lines are measured. The opposite angles have the same size, regardless of the movement of the lines. The diagram helps us to see why this must be the case ... since the pair of angles that comprise any line must necessarily add to 180 degrees. Each of the opposite angles must be the difference between 180 degrees and the other angle. Try the Angles applet for yourself.

Two Angles in a circle are formed from points on the circle. The diagram helps us to see the congruence of the angles, regardless of the choices of points. Try the Angles in a circle applet for yourself.

Two Parallels are intersected by a transversal line, resulting in several angles. The applet allows you to see which angles are congruent. Try the Parallels applet for yourself.

When the midpoints of the sides of a Quadrilateral are joined, another quadrilateral results. using the diagram helps to see what is special about this new quadrilateral. Try the Quadrilateral applet for yourself.

The Pythagorean Theorem can be proved in many ways. This diagram uses shears to show a version of Euclid's proof. The applet is a slight variation on the one provided by the publishers of GSP. Try the Pythagorean Theorem applet for yourself.

Trig tracers show the paths of points on a circle, leading to sine and cosine curves. The applet is a slight variation on the one provided by the publishers of GSP. Try the Trig tracers applet for yourself.

Vertically opposite angles are formed by a pair of intersecting lines. By manipulating the lines, the sizes of the angles can be compared. Try the Vertically opposite angles applet for yourself.

When an object is subjected to Two reflections , there are various possibilities for the composite transformation. These can be seen by manipulating the reflections as well as the original object. Try the Two reflections applet for yourself.