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 600
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 00 but less than 900 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 900, 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 900
- 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 900 and each one of the remaining two angles is acute.
Obtuse-angled triangle:
- A triangle in which one of the angles measures more than 900 but less than 1800, 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.