Introduction To Triangles

Triangles Introduction Mark three non-collinear point P, Q and R on a paper. Join these pints 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, Triangle PRQ, Triangle QRP, Triangle RPQ

or Triangle RQP .

Triangle A triangle is a polygon of three sides. In fact, it is the polygon with the least number of sides. A triangle PQR consists of all the points on the line segment PQ, QR and RP. 1. Sides: The three line segments, PQ, QR and RP that form the triangle PQ, are called the sides of the triangle PQR. 2. Angles: A triangle has three angles. In figure 4-1, the three angles are ∠PQR, ∠QRP and ∠RPQ .

3. Parts of triangle: A triangle has six parts, namely, three sides, PQ, QR, and RP , and 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 4-1, 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. Classification of Triangles Triangles can be classified in two groups: A. Triangles differentiated on the basis of their sides. 1. Equilateral Triangles: A triangle with all sides equal to one another is called an equilateral triangle. Here, PQ = QR = RP

Therefore Triangle PQR is an equilateral triangle

2. Isosceles Triangle: A triangle with a pair of equal sides is called an isosceles triangle. Here PQ = QR

Therefore Triangle PQR is an isosceles triangle

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. Here PQ ≠ QR ≠ PR

Therefore Triangle PQR is an scalene triangle

B. Triangles differentiated on the basis of their angles. 1. Acute angled triangle. A triangle whose all angles are acute is called an acute-angled triangle or simply an acute triangle.

2. Right-angled triangle. A triangle whose one of the angles is a right angle is called a right-angled triangle, or simply a right triangle.

The side opposite to the right angle is called Hypotenuse and the other two sides are called the legs of the triangle. In a right triangle, hypotenuse is the greatest side. 3. Obtuse-angled triangle. A triangle one of whose angles is obtuse is called an obtuse-angled triangle or simply an obtuse triangle.

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