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Definition Parts of a Triangle

Definition A triangle is a polygon with exactly three sides. Because it is a polygon, it follows that it also has three vertices and three angles. Parts of a Triangle Adjacent The two sides of a triangle which form a particular vertex are referred to as adjacent to that angle. Similarly, the two vertices of a triangle to which a particular side contributes are referred to as adjacent to that side. Opposite The side of a triangle which is not one of the sides adjacent to a particular vertex is referred to as its opposite. Thus, each vertex has an opposite side, and each side has an opposite vertex. Base For a given triangle, one of the sides can be distinguished as being the base. It is immaterial which is so chosen. The usual practice is that the triangle is drawn so that the base is made horizontal, and at the bottom. In the above diagram, it would be conventional for the side AC to be identified as the base. Apex Having selected one side of a triangle to be the base, the opposite vertex to that base is called the apex. In the above diagram, if AC is taken to be the base of △ABC, then B is the apex. Height The height of a triangle is the length of a perpendicular from the apex to the base. Conventional Nomenclature The vertices of a triangle are conventionally labeled A,B,C (or with other uppercase letters), and the sides with lowercase letters corresponding to the opposite vertex, as above. In order to emphasize that a particular vertex being referred to is in fact a vertex, the symbol ∠ is often placed by the letter corresponding to that vertex. Thus, for example: ∠A is adjacent to sides b and c Side a is adjacent to ∠B and ∠C ∠A is opposite side a Side a is opposite ∠A. Types of Triangle Isosceles Triangle An isosceles triangle is a triangle in which two sides are the same length. Equilateral Triangle An equilateral triangle is a triangle in which all three sides are the same length: That is, a regular polygon with 3 sides. Scalene Triangle A scalene triangle is a triangle in which all three sides are of different lengths. Right-Angled Triangle A right-angled triangle is a triangle in which one of the vertices is a right angle. Note that in order to emphasise the nature of the right angle in such a triangle, a small square is usually drawn inside it. Oblique Triangle An oblique triangle is a triangle in which none of the vertices are right angles. Acute Triangle An acute triangle, is a triangle in which all three of the vertices are acute angles. Obtuse Triangle An obtuse triangle is a triangle in which one of the vertices is an obtuse angle.