For 10 points, name this simple shape, whose area is calculable by Heron's formula and whose angles add up to 180 degrees.
Napoleon's theorem concerns the use of four of these figures to construct a fifth with special properties, and a similar method is used to locate the Fermat point for this shape. Nine significant locations on it are traversed by the nine-point circle, the center of which lies on an Euler line in this shape. Ceva's theorem concerning this shape states that lines drawn from a vertex to a side meet under certain conditions, and another statement about it allows its area to be determined from side length and semiperimeter alone. For 10 points, name this simple shape, whose area is calculable by Heron's formula and whose angles add up to 180 degrees.
Napoleon's theorem concerns the use of four of these figures to construct a fifth with special properties, and a similar method is used to locate the Fermat point for this shape.
triangle