[Math Lair] Triangles

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A triangle is a polygon having three sides and three interior angles. The interior angles of a triangle always sum to 180°.

Triangles can be classified in a few ways. One way to classify them is by the number of sides of equal length:

Triangles can also be classified by the measurement of their largest angle:

Triangles have many important practical applications. A triangle, unlike other polygons, is rigid. You can see this for yourself if you get some straws and some large marshmallows. If you make a triangle by taking three straws and attaching them at each vertex using balls of clay or large marshmallows, you will find that the shape is rigid; you cannot deform it by pushing or pulling the sides. On the other hand, if you construct a square using four straws and four marshmallows, you can easily deform it. Because of the sturdiness of triangles, they are used frequently in construction. To take one example out of many, a truss bridge will be comprised of a large number of triangles.