Triangles : Construction and Properties - Part II

3. Types of triangles 
There are three types of triangles :

1. Equilateral triangle
2. Isosceles triangle
3. Right angled triangle
4. Other triangles

Equilateral triangle :  When all the sides of the triangle are equal, the triangle is said to be an equilateral triangle.  It is interesting to note that the three angles of the triangle also become equal and each has a value of 60ƒ.  

l(AB) = l(BC) = l(AC)  ABC is an equilateral triangle. A = B  =  C = 60ƒ

Isosceles triangle : When two sides of a triangle are equal, the triangle is said to be an isosceles triangle.  The two angles formed by these two sides with the third side, turn out to be equal to each other. 

l(BC) = l(AC) ABC is an isosceles triangle. A = B

Right angled triangle : When one of the angles of the triangle is 90ƒ, the triangle is called a right angled triangle. The side opposite to the right angle is called the hypotenuse of the triangle. It is interesting to note that the sum of the remaining two angles has to be 90ƒ only.  

A = 90ƒ . The symbol for such an angle is a sharp corner as shown. Side BC is called the hypotenuse ABC is a right angled or a right triangle.

Other Triangles :Besides the equilateral, isosceles and right angled triangles, there are three other types of triangles : acute angled triangles, obtuse angled triangles and scalene triangles.  

As the name suggests, acute angles triangles have all angles < 90ƒ. In obtuse angled triangle, one angle is obtuse that is > 90ƒ, and the other two are acute and are < 90ƒ. In a scalene triangle, the sides and angles are such that none of the altitudes from each vertex match.  

4. Other definitions
In the discussions above, we have seen the definitions of altitudes of a triangle, perimeter and semi-perimeter of a triangle, area of a triangle, etc. There are a few other definitions associated with triangles that have to be learnt as they are often referred to. They are median and orthocentre of a triangle.

Median : Consider  ABC.  Find mid point D of the Segment AB.   l(AD) = l(DB)

Join Vertex C to point D. Segment CD is known as the median. A median can be drawn from any of the vertices. Thus a given triangle will have three medians.  

Orthocentre of a triangle : In ABC,  from each vertex, drop a perpendicular to the opposite side.

Seg CD seg AB, seg AE seg BC, seg BF   seg AC. The point O where the three perpendiculars CD, AE and BF intersect is known as the orthocentre of the triangle.

For a right angled triangle PQR shown, the orthocentre will be the vertex Q. For an obtuse angled triangle, the orthocentre will fall outside the triangle.

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