# Triangles

A polygon is a closed figure drawn with the help of line segments only. In other words, we can say that polygons are rectilinear figures. The line segments with the help of which they are drawn are called the sides or edges of the polygon. The points where two line segments meet to enclose a figure are termed as the vertices or the corners of the polygons & the two sides meeting at a vertex form an angle. Thus, polygons are closed rectilinear figures with a number of sides, vertices & angles.

Turning to the definition of triangle, tri means three. Thus, a triangle is a polygon with 3 sides. It means it is a closed figure made up of 3 line segments. A triangle, as the name itself explains, has three angles. Thus, we can give following points regarding triangles:

They have 3 sides.

They have 3 angles.

They have 3 vertices.

Further, we have two basis of classification of triangles, viz., measure of the length of their sides & measure of their angles. Let us know about Triangles & their classification in detail.

On the basis of measure of the length of the three sides of triangles, the triangles may be put under the following 3 classes:

Scalene triangles: When the measure of all the sides of a triangle is different, i.e., all the sides of a triangle are unequal, it is called scalene triangle.

Isosceles triangles: When any two of the sides of a triangle are equal & the third side is unequal, such a triangle is called isosceles triangle.

Equilateral triangle: When all the sides of a triangle are of equal length, it is called an equilateral triangle.

Classification of triangles on the basis of measure of the three angles of the triangles, the triangles can be put under three classes as follows:

Acute angled triangle: When all angles of a triangle are acute angles, i.e., they all measure less than 90  ̊, it is called an acute angled triangle .

Right angled triangle: When one of the angles of a triangle is right angle, i.e., exactly 90  ̊& other two angles are acute angles, it is called a right angled triangle.

Obtuse angled triangle: When one of the angles of a triangle is obtuse angle, i.e., more than 900 & other two angles are acute angles, it is called an obtuse angled triangle.

It is worth mentioning here that the sum of all the angles of a triangle is exactly 1800.

## Congruent Figures

If two geometrical figures have exactly the same shape and size then they are called
congruent figures.
PQ ≅ RS

Points to Remember:
a) Two line segments are congruent only when their lengths are equal.