SSC LDC GURU 2014: Triangle and its various kinds of centres

TRIANGLES

A triangle has three sides and three angles. The sum of the angles are always 180^o.

Mark three non-collinear point P, Q and R on a paper. Join these points in all possible ways.

The segments are PQ, QR and RP. A simple close curve formed by these three segments is called a triangle. It is named in one of the following ways.

Triangle PQR or Triangle PRQ or Triangle QRP or Triangle RPQ or Triangle RQP .

A triangle is one of the basic shapes of geometry. It can be defined as a polygon with three corners or vertices and three sides or edges which are line segments. It is the polygon with the least number of sides.

A triangle has three angles. In figure, the three angles are ∠PQR ∠QRP and ∠RPQ (in the figure)

In other words we can say that, a triangle has six parts, namely, three sides (PQ, QR and RP).Three angles ∠PQR, ∠QRP and ∠RPQ. These are also known as the elements of a triangle.

Vertices of a Triangle

The point of intersection of the sides of a triangle is known as its vertex. In figure, the three vertices are P, Q and R. In a triangle, an angle is formed at the vertex. Since it has three vertices, so three angles are formed. The word triangle =tri + angle ‘tri’ means three. So, triangle means closed figure of straight lines having three angles.

Types of Triangles by Length

1. Equilateral Triangles: A triangle with all sides equal to one another is called an equilateral triangle. An equilateral triangle is always equiangular.

2. Isosceles Triangle: A triangle with a pair of equal sides is called an isosceles triangle. An isosceles triangle may be right, obtuse, or acute.

3. Scalene Triangle: A triangle in which all the sides are of different lengths and no two sides are equal, the triangle is called a scalene triangle.

Types of Triangle by Angle

1. Equiangular triangle : In an equiangular triangle, all the angles are equal— each one measures 60 degrees. An equiangular triangle is a kind of acute triangle, and is always equilateral.

2. Right triangle : In a right triangle, one of the angles is a right angle—an angle of 90 degrees. A right triangle may be isosceles or scalene.

3. Obtuse triangle : In an obtuse triangle, one angle is greater than a right angle—it is more than 90 degrees. An obtuse triangle may be isosceles or scalene.

4. Acute Triangle : In an acute triangle, all angles are less than right angles—each one is less than 90 degrees. An acute triangle may be equilateral, isosceles, or scalene.