Excerpt from Some Noteworthy Properties of the Triangle and Its Circles
1. The triangle is the only rigid figure; that is to say, it is the only polygon whose sides alone determine its shape and size, or whose angles determine the ratio of its sides and of all other parts.
2. Every triangle has three sides, three angles, three altitudes, three medians, three interior angle bisectors, three exterior angle bisectors, and three perpendicular bisectors of its sides. In addition to these parts of every triangle, there are certain other lines and circles dependent upon these parts; and their mutual relations and the variety of their interdependencies are fascinating to the student just awakening to the beauties of the science of geometry.
3. In general, a triangle is determined by any three of its parts, one of these parts being a length, whether this length be a side, an altitude, the radius of any one of its numerous dependent circles, or any other length.
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