Triangles: SketchPad Files
(1). On opening any of these scripts enclosed in the above pages you may not actually see them! - What you may see instead is a blank Sketch File probably called "Sketch01.gsp". If you are unfamiliar with SketchPad all that you need to do is to click on the "Restore" Button in the top right of the active Sketch file Window Toolbar.
(2). All of these filenames in this page are LONG! - Therefore, if you want to preserve these (Because Version 3.* of SketchPad does not use long filenames) you must either RIGHT-CLICK on the file links within the above directories and then choose "Save Target As...". This allows you to save the file directly to a disk/drive or after using a LEFT-CLICK select the "Save this file to disk" Option Box rather than selecting the "Open this file from its current location". If you choose this last option then Geometer's SketchPad will automatically open - if you have it! - but then after viewing the file if you then try to save it you will not be able to use a long filename.
D - Gergonne Point Construction.gss
This script constructs the Gergonne Point in a given triangle.
The Gergonne Point is the intersection point of each of the three cevians from the point of tangency of the incircle to a triangle side to its opposite apex, repectively
D - Medial Triangle.gss
An interior triangle formed from the mid-points of the sides.
D - Median Lines Triangle Construct.gss
A new triangle is constructed from 'extracting' the median lines from the given triangle.
D - Nagel Point Construction.gss
D - Nine Point Circle Centre Construction.gss
D - Nine Point Circle Construction.gss
D - Nine Point Circle Contruction and Full Labelling.gss
D - Orthic Triangle Construction (Basic).gss
D - Pedal Triangle - Circle Investigation.gss
Drop perpendiculars from the ponit D to each side (possibly extended) of the triangle. Join these intersection points to form the Pedal Triangle.
Before you run the script with your 4 points you could experiment by adding a circle and placing the point D on the circumference on this circle. Then once the Pedal Triangle has been constructed try moving the point D around its circle. In another experiment you could put the point D on the Circumcircle of the Triangle ABC before running the script.
Try constructing the Orthocentre of the Pedal Triangle, highlight it and press "Ctrl+T " - this will put a 'Trace' on this Orthocentre which can be followed as the point D is moved.
D - Berzsenyi Triple Circle Concurrency.gsp
All three circles always meet at a single point and behind this property is a beautifully symmetric set of formulae.
D - Carnot's Theorem.gsp
Met above in Japanese Temple Geometry - A most useful Theorem.
D - Ceva's Theorem (Triangle Side Ratios).gsp
A fundamental Theorem with many hidden applications especially in proving many Triangle Centre Theorems
D - Collinearity Property of Exterior Angle Bisectors and Sides.gsp
An interesting property of extended sides and exterior angle bisector lines.
D - Collinearity Property of Orthocentres of 4 Arbitrary Lines.gsp
An amazing Theorem - and it looks particularly complicated! However, it can be simplified and explained a step at a time with Show/Hide Buttons.
D - Collinearity Property of Triangle with 3 Parallelograms.gsp
Met above in 'Quadrilaterals' page - still amazing!
D - Desargue 2D Concurrency.gsp
Desargues Theorem says that if corresponding sides of two triangles meet in three points lying on a straight line, then corresponding vertices lie on three concurrent lines.
D - Desargue 3D Projection.gsp
A further application of the above Theorem which is a fundamental theorem behind Vanishing points and Perspective.
D - Droz-Farny Theorem.gsp
D - Halving a Triangle.gsp
Full details given
D - Incircle Sequence.gsp
D - Miquel Triangle.gsp
Three Theorems in one here. A very nice animation.
D - Napoleon Point Investigation.gsp
A well known result.
D - Pedal Triangle Construction.gsp
D - Simpson Line - Definition.gsp
Another remarkable collinear condition.
D - Simson Lines - Interactive Sketch.gsp
A second animated version of the above.
D - Triangle Side and Cevian Ratios.gsp
Three remarkable Theories relating to cevians and sides in any Triangle - One of my favourites!
D - Pedal Area Property.gsp
A lovely area thoerem to amaze people with. The sum of the areas of the Red squares is equal to the sum of the Green squares for any position of the general point P. See a paper by Jean-Pierre Ehrmann and Floor van Lamoen for this and more interesting properties