*Open Figures**: **Figures which have different initial and end points are called open figures.*

*If starting point and the end point of a figure are not same, then the figure is an Open Figure.*

*Closed Figure :-** If starting point and the end point of a figure are same, then the figure is a Closed Figure.*

*Figures in which initial and end points coincide with each other are called closed figures**. *

*Simple Curves: **The curved lines that do not intersect themselves are called simple curved lines.*

*A simple curve is a curve that does not cross itself.*

Simple Closed Figures :-

A connected **curve** that does not cross itself and ends at the same point where it begins.

Examples are circles, ellipses, and polygons.

**not Simple Closed Figures**

** Triangle :-**

** A triangle is a simple closed figure consisting of three line segments.**

** A closed plane figure bounded by three line segments is called a triangle.**

** let A, B and C be three non-collinear points. **

*Then, the figure formed by the three line segments AB, BC and CA is called a triangle ABC, denoted by**.*** * We denote a triangle by the symbol Δ **

*In ∆ABC *

*has*

*Three vertices, namely A, B, C**Three sides, namely AB, BC and CA**Three angles namely**∠**A,∠B, ∠C**The sides BC , CA and AB are denoted by a, b and c*

*In a triangle ABC, side AB and AC meet at A.**the remaining side BC is the opposite side of vertex A.**also A is the vertex opposite side BC.*

*In * *the points A, B and C are called its vertices.*

** Clearly **A is the vertex opposite to the side BC.*

** B is the vertex opposite to the side CA, and *

** C is the vertex opposite to the side AB.*

**The three sides and the three angles are known as the six elements or parts of the triangle.**

** The lengths of the sides of a triangle can be measured by a scale and the angles by a Protector.**

* *

*A triangle divides a plane in which it lies into three sets of points.*

* *

*The set of point in the interior of the triangle.**The set points on the triangle and**The set of points in the exterior of the triangle.*

*Classification of triangles according to sides.*

** Triangles can be divided into three kinds according to the measures of their sides, **

*as follows**Scalene triangle,**Isosceles triangle,**Equilateral triangle.*

**Scalene triangle:**

**If all the three sides of a triangle are of different lengths, then the triangle is called a scalene triangle.****A triangle having all side of different lengths, is called a Scalene triangle.***ABC is a triangle in which**AB≠BC≠CA then ∆ABC is a scalene triangle.**All the three angles f a scalene triangle are of different measures.*

*Isosceles triangle:-*

*A triangle having two sides of equal length is called an isosceles triangle.**If any triangle contains two sides of equal measures, such triangle is called an isosceles triangle.**In isosceles triangle, the angles opposite to the equal sides are equal.**In an isosceles triangle the unequal side is called the base of the triangle.**The angles contained by the base are called base angles.**The base angles of an isosceles triangle are congruent.*

*Equilateral triangle*

*A Triangle having all the three sides equal,**is called an equilateral triangle.**The measure of each angle of an equilateral triangle is**60*^{0}

*Classification of triangles according to angles**.*

*Acute angle Triangle**Right angled Triangle**Obtuse Angle Triangle*

**Acute angled triangle :- **

**A triangle in which every angle measure****more than 0**^{0 }but less than 90^{0}is called an acute angled triangle.**A triangle with all the three angles**

acute is called an acute angled triangle.

**Right angled Triangle :-**

**A triangle in which one of the angles measures 90**^{0}, is called a right angled triangle or simply right triangle.**A triangle having one right angle is called an right- angled triangle.****A Triangle is called right angled triangle,****if the measure of one of its angle is 90**^{0}**In right angled triangle , the opposite side of the right angle is****called its hypotenuse and the remaining two sides are called it legs.****In a right angled triangle, one angle measures 90**^{0 }and each one of the remaining two angles is acute.

*Obtuse-angled triangle:*

*A triangle in which one of the angles measures more than**90*^{0}but less than 180^{0}, is called an obtuse angled triangle.*A triangle having one obtuse angle is called*

an obtuse angled triangle.*In obtuse angled triangle, one of the angles is obtuse angle**and each one of the remaining two angles is*

acute angles.