Triangles

Triangles

What is a Triangle??

A three sided closed figure is called a Triangle.

Triangles:

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC.

Types of Triangles:

Classification of Triangles:

Triangles can be classified according to the relative lengths of their sides:

• In an equilateral triangle all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.
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• In an isosceles triangle, two sides are equal in length.
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• An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the Isosceles triangle theorem. Some mathematicians define an isosceles triangles to have only two equal sides, whereas others define that an isosceles triangle is one with at least two equal sides.
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• The latter definition would make all equilateral triangles isosceles triangles
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• In a scalene triangle, all sides are unequal
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• The three angles are also all different in measure. Notice that a scalene triangle can be (but need not be) a right triangle.

Triangles are assumed to be two-dimensional plane figures.

A few basic theorems about similar triangles:

• If two corresponding internal angles of two triangles have the same measure, the triangles are similar.
• If two corresponding sides of two triangles are in proportion, and their included angles have the same measure, then the triangles are similar. (The included angle for any two sides of a polygon is the internal angle between those two sides.)
• If three corresponding sides of two triangles are in proportion, then the triangles are similar.

Two triangles that are congruent have exactly the same size and shape:all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. (This is a total of six equalities, but three are often sufficient to prove congruence.)