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A close figure, formed by straight lines is called a polygon in plane geometry. Triangle is a polygon with three sides. The literal meaning of triangle is, having three angles. The sum of three angles being 180 degrees.

Types of triangles

1.Based on interior angles of triangle.

i)Right angled triangle- In this triangle one angle is of ninety degrees and the remaining two are acute angles(less than ninety degrees).The side opposite right angle is called hypotenuse, the longest side of the triangle.

One of the important theorems in geometry, given by greek mathematician Pythagoras states- square of hypotenuse = square of base + square of height (base, height and hypotenuse being three sides of triangle)

ii)Acute angled triangle- Each of the three angles of the triangle are less than ninety degrees, but the sum total of three angles is always 180 degrees.

iii)Obtuse angled triangle- One of the angles is obtuse, that is greater than ninety degrees and the remaining two are acute angles. The side opposite obtuse angle is longest while the side opposite smallest angle is minimum in length.

2.Based on dimension of three sides.

i)Equilateral triangle - In this type of triangle all three sides of the triangle are equal in length. Each angle of the triangle is sixty degrees; hence it is also known as equiangular.

ii)Isosceles triangle- Any two angles of the triangle are equal in dimension hence the side opposite them are also equal.

iii)Scalene triangles- Triangles in which all three sides have a different measure.

Perimeter of a triangle
Perimeter is sum of three sides of a triangle. Perimeter = a+b+c; where a, b, c are three sides of a triangle.

Area of a triangle - Different formulas are applicable to different types of triangle. The most fundamental being Area = 1/2*b*h. Area = square root(S(S-a) (S-b) (S-c)) where S is the semi perimeter S = (a+b+c)/2 where a, b, c are three side of the triangle. This formula is used for a scalene triangles.

Similar triangles - Two triangles are said to be similar if, the three corresponding sides are proportional and secondly two pairs of corresponding angles are congruent. Basically two triangles are said to be similar if they have the same shape by virtue of its angles though the size(area) may vary.

Congruent triangles

Triangles are said to be congruent if they have same shape and size.There are several rules to prove congruency of triangles.

SSS -If all the three sides of a triangle are equal to the corresponding three sides of another triangle then the two triangles are said to be congruent.

SAS If two sides and included angle of one triangle is equal to the two sides and included angle of another triangle then the triangles are said to be congruent.

AAS If two angles and a side of one triangle is equal to two angles and non-included side of another triangle then the triangles are said to be congruent.

I have briefly touched , the basics of triangles, that is different kinds of triangle, perimeter, area, similarity and congruency. But in my opinion , any concept of mathematics is best understood by examples and requires ample self practice.

Learn more about this author, Tanu Bhandari.
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