![]() ![]() You may see diagonal wires used to keep bridges steady. Diagonals in real lifeĭiagonals in squares and rectangles add strength to construction, whether for a house wall, bridge, or tall building. Diagonals In Concave Polygonsĭo not attempt to apply these concepts and our diagonal formula to complex polygons (polygons with self-intersecting lines). Darts and stars are typical examples of concave polygons with diagonals outside their shapes. In concave, simple polygons, the diagonals may go outside the polygon, crossing sides and partly lying in the shape's exterior. Those are the only two diagonals possible. You can also run a line from the bottom hinge corner up to the top, opposite corner. You can run a line from the top hinge corner to the bottom, opposite corner. ![]() In convex, simple polygons, diagonals will always be within the interior. A pentagon, whether regular or irregular, has five diagonals. A quadrilateral, the next-simplest, has two diagonals. You cannot draw a line from one interior angle to any other interior angle that is not also a side of the triangle. So a triangle, the simplest polygon, has no diagonals. What's a diagonal?Ī diagonal of a polygon is a line from a vertex to a non-adjacent vertex. The formula we will use works for all simple polygons. Simple polygons can be concave or convex. A dart, kite, quadrilateral, and star are all polygons. A simple polygon is any two-dimensional (flat) shape made only with straight sides that close in a space, and with sides that do not cross each other (if they do, it is a complex polygon). ![]()
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