The Basics About Triangles
The most basic definition of a triangle is that it is a geometric shape that has three sides. If all sides are the same length, then it is called an Equilateral triangle. There are other possibilities for different triangle shapes, depending on the lengths of each of the three sides and the angles.
Following is a basic list of some triangle types.
Some Types of Triangles:
Acute
Equilateral
Isosceles
Obtuse
Right
Scalene
A Brief Description of Each Type:
In an Acute triangle, all three angles are less than 90 degrees.
In an Equilateral triangle, all sides have the same length, with equal angles that are always 60 degrees.
In an Isosceles triangle, two sides are exactly the same in length and there are two equal angles.
An Obtuse triangle has one angle that is greater than 90 degrees.
A Right triangle has the characteristic of having one 90 degree angle. One of the sides is called a hypotenuse, which is the longest side and is also the side opposite to the right angle.
In a Scalene triangle, all sides do not measure the same and there are no equal angles.
Now and then, a triangle will have more than one of these types within that triangle, so it will have a combination of the two names as a type, for instance, a Right Isosceles Triangle.
Formulas
There are assorted formulas for figuring the area or height of a triangle, using vectors, trigonometry, coordinates, Heron’s formula, Pick’s Theorem.
Trigonometry
In Trigonometry the Sine, Cosine and Tangent functions are a side of a triangle divided by another side of the same triangle. Each side has a name, for example, a right-angled triangle has an adjacent side, a hypotenuse side and an opposite side.
Geometry
What does geometry have to do with triangles? Geometry is about shapes and the properties of each shape. Plane Geometry is about flat shapes, so if you drew a triangle on a piece of paper, that would be an example of plane geometry. The other type is Solid Geometry, which, in relation to triangles, would be a triangle that is three dimensional.
Within the Solid Geometry type, there are other categories and sub-categories; in Polyhedra, there are Platonic Solids, Prisms and Pyramids (which have flat surfaces). Relating more to shapes other than the triangle, in Solid Geometry there are also Non-Polyhedra shapes, divided into categories of the cone, cylinder, sphere and torus (where any surface is not flat).
All triangles are convex and bicentric. The name convex is used for polygons, which are either convex or concave. The term bicentric means that the shape has both an incircle and a circumcircle. An incircle is a circle that touches each of the triangle’s three sides (this circle is inside the triangle, with the edge of the circle touching the inside edges of each of the triangle sides). A circumcircle is a circle that passes through each of the triangles three vertices (this circle is on the outside of the triangle, with the three points of the triangle touching the inside edge of the circle).
The term vertices is the plural of vertex. Vertex means a corner point of any 3-D shape.
These are only the basic terms used in math, geometry and trigonometry in relation to triangles. If you have an interest in the subject, there is much more that you can explore. Your local library in all probability will have some good books on this topic.
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