In this post we will cover the Basic properties of a common triangle and then will cover the topic of different types of triangles including Isosceles Triangle, Right angled triangle and Equilateral triangle.
You can also read some other related post to this topic at
Basic properties of all types of triangles
1. Sum of all the three angles of a triangle is 180o
2. The exterior angles is formed when side of triangle is extended further from the vertex and angles is formed between extended side and side touching it on vertex. The angle formed inside the triangle is called internal angle
3. There can be at most 6 exterior angles of a triangle, 2 each can be formed at the vertex bt extending 2 sides of the vertex.
4. Sum of internal angle and exterior angles is equal to 180o
5. Sum of any 2 sides is greater than third side and sum of any 2 internal angles is always greater than third side
BC < AB + AC
6. In any triangle, there can be only one right angle or only one obtuse angle. This means a triangle must have atleast 2 acute angles
In an isosceles triangle, 2 sides are equal. Since the 2 sides are equal the line that divides the angle included between 2 sides is also bisects the opposite side at right angle, hence this line is a perpendicular bisector as well as median of the base.
In the diagram Line AD is median and perpendicular bisector
Right angled Isosceles Triangle
In such type of isosceles triangle the included triangle is 900 where as the acute angles are 450 each . Thus we can have
Hypotenuse = \/2 x one side ( Both the sides are equal)
For general Right angled triangles where one angle is 90o where as other 2 angles can be anything as long as they sum to 90o.
c2 = m(m+n) , b2=n(n + m), h2 = mn
c and b are sides of triangle, a is hypotenuse, h is altitude of RA triangle
2 x Radius of circumcircle ( Circle touching all the vertex of right angled triangle) = Hypotensue
Radius of incircle = bc/(a+b+c)
As per Pythagoras Theorem = Square of base ( hypotenuse) x Sum of the squares of the other 2 sides
to refer to Pythagoras triplets please refer an earlier post over here >> Click here
Special Right angled Triangle – with angles as 30-60-90
In this case since the sides can be represented in proportion, if side opposite to 30o is a, 60o will be 2a and 900 will be 3a, hence we can say from the diagram
The triangle where all sides are equal and included angles are also equal, please refer to this earlier post for all details and formulae on Equilateral triangles >> Click here
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