# Types of triangles and Polygons A triangle is a three sided closed figure·

A triangle whose all the sides are unequal is called a scalene triangleAll the three angles will also be different in this case. AB ¹ BC ¹ AC

·                     A triangle, two of whose sides are equal in length is called an isosceles triangle.In this case  two angles will be of equal measure and one will be different. AB = AC ¹ BC

B = ∠ ¹  A

·                     A triangle, all of whose sides are equal is called an equilateral triangle.All the three angles will be equal in this case and each of them will be of 60 degree measure. AB = BC = AC

A = B = C = 60°

·                     A triangle, each of whose angles is less than 90°, is called an acute angled triangle.

Acute Angle triangle ·                     A triangle with one of its angle 90° is called a right angled triangle. ·                     A triangle with one of its angle greater than 90° is known as an obtuse angled triangle.

Obtuse Angle triangle If a side of a triangle is produced, the exterior angle so formed is equal to the sum of two interior opposite angles. x = A + B

A + B +C = 180°                         ....(1)

C + x = 180° (linear pair)              ....(2)

From (1) & (2)

x = A + B

Important : The angle opposite to biggest side is the biggest and the angle opposite to smallest side is the smallest.

Polygons

·                     If all sides of a polygon are equal, it is called a regular polygon. ·                     A six-sided figure is called a hexagon.

·                     A seven-sided figure is called a heptagon.

·                     An eight-sided figure is called an octagon, etc.

Theorem 1:

·           In a convex polygon of n sides, the sum of the interior angles is equal to (2n – 4) right angles.

Theorem 2:

·           In a convex polygon of n sides, the sum of the exterior angles, sides produced in order, is equal to 4 right angles.

·                     If ‘n’ be the number of sides.

Each interior angle = (2n-4)/n right angles.

·                     Sum of all the interior angles of a polygon of n sides = (n – 2) x 180° where (n ³ 3)

For          n = 3 (Triangle) Þ 180°

n = 4 (Rectangle) Þ  2 x 180° = 360°

n = 5 (Pentagon)  Þ  3 x 180° = 540°

n = 6 (Hexagon) Þ  4 x 180° = 720°

·                     Each interior angle of a regular polygon having n sides = (n – 2) x 180°/n

For          n = 3 (Triangle) Þ 60°

n = 4 (Rectangle) Þ 90°

n = 5 (Pentagon)  Þ 108°

n = 6 (Hexagon) Þ 120°

·

Sum of all the exterior angles formed by producing the sides of polygon = 360°

a + b + c + d + e + f = 360° ·                     Number of sides of polygon = 360°/ ( 180°- each interior angle)