Triangle Dissections  We all know that you can cut (or ‘dissect’) a square into 4 equal, but smaller, squares.  These are ‘self-similar’ to the original square - the same shape, but a different size. You can do a similar thing to create a diagram with 9 smaller squares.  Can you do the same thing, dissecting any triangle into 4 smaller self-similar triangles, using a similar approach ?  Problem Set 1  Starting with the rather special triangles shown below - the 30°, 60°, 90° triangle that is half an equilateral triangle, and the ‘half-domino’ triangle - there are 2 nice challenges along similar lines ... :   A         Can you show how to dissect the first into just 3 smaller self-similar triangles ? B         Can you show how to dissect the second into 5 smaller self-similar triangles ?  Problem Set 2  Starting with an equilateral triangle, can you show how to dissect it into : C         12 identical triangles (not necessarily equilateral) D         13 equilateral triangles (not necessarily all the same size)  E         14 triangles of the same area (but not necessarily the same shape)            F          15 equilateral triangles (not necessarily all the same size) G         16 equilateral triangles. Open the File as a Word Document