Revision Notes on Triangles

Learning Goal

Triangle

1. Part of Triangle- Vertex, Sides, Angles
2. Interior and Exterior of triangle
3. Type of Triangles -6
4. Properties of triangle

Introduction to Basic Geometrical Ideas

The term ‘Geometry’ is derived from the Greek word ‘Geometron’. This has 2 equivalents. ‘Geo’ means Earth and ‘metron’ means Measurement.

Triangle

A closed curve figure made up of three-line segments is called triangle.

It has three vertices, three sides and three angles.

Here, in ∆ABC,

AB, BC and CA are the three sides. It is also represented as c, a and b respectively.

A, B and C are three vertices.

∠A, ∠B and ∠C are the three angles.

Types of Triangles on the basis of sides

Types of Triangles on the basis of angles

Here, the light blue coloured area is the interior of the triangle.

The black line is the boundary.

Whereas, the dark blue area is the exterior of the triangle.

1. Equilateral triangle : – A triangle whose all sides are equal is called Equilateral triangle.

                  

Properties : – It’s all sides are equal.    AB = BC = CA                                  

It’s all angles are equal.   ∠A = ∠B = ∠C = 60°  OR ∠CAB=∠ABC=∠BCA = 60°  

Area of equilateral triangle = (side)² = (a)²              

Perimeter = 3 × side

2. Isosceles triangle : – A  triangle whose two sides are equal is called Isosceles triangle.

Properties : – It’s two sides are equal AC = BC                                        

   It’s base angles are equal ∠A=∠B                                                 

3. Scalene triangle : – A triangle whose sides are not equal is called Scalene triangle.   

Properties : – It’s all sides are unequal.      AB ≠  BC ≠  CA                    

  It’s all angles are unequal   ∠A  ≠  ∠B  ≠  ∠C   

4. Right angled triangle: – A triangle whose one angle is right  (θ=90° ) angle is called Right angle triangle.                   

The opposite side of right angled ∆  is called hypotenuse(h).

In fig BC is hypotenuse, AB is base(b) on which it bases and AC is perpendicular(p).

5. Acute angled triangle: – A triangle whose all angles are acute (0°< θ < 90°  ) is called acute angled triangle.

6. Obtuse angled triangle: – A triangle whose one angle is obtuse angle (90° <θ < 180°  ) is called obtuse angled triangle.