A triangle is a three sided closed figure·

A triangle whose all the sides are unequal is called a **scalene triangle**. All 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 = ∠ C 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)