Properties of triangles deals with relation between sides and angles of a triangle.
Theorem: The sides of a triangle are proportional to the sines of the angles opposite to them, given by
where a, b, c are the sides of the triangle, A, B, C are the angles of the triangle, is known as sine rule.
A Circle that passes through all the three vertices of a triangle is known as circumcircle and the point of concurrency of the bisectors of the sides of the triangle is known as circum centre, the distance from circum centre to any one vertex of the triangle is known as circum radius given by "R".
Theorem: The square of side of the triangle is equal to sum of the squares of other two sides subtracted by the product of 2 and other two sides and also cosine of opposite angle.
a2 = b2 + c2 - 2bc cosA, b2 = c2 + a2 - 2ac cosB,
c2 = a2 + b2 - 2ab cosC
Theorem: We know that the altitude of a triangle is always perpendicular to the base, the trigonometric ratio sine can be written as
Opposite side to 
= sin × hypotenuse which gives the altitude of the triangle.
Theorem: Using sine rule the auxiliary formula that can be derived is known as Napier's Analogy given by
Theorem: The relation between the sides of a triangle and sine and cosine functions is given by Mollweide rule given by
Theorem: If s is semi perimeter of a triangle, it is given by 
, area of the triangle is given by
¤ A circle that touches all the sides of a triangle internally is known as incircle, the point of concurrency of the angular bisectors of the sides of a triangle is known as incentre, the perpendicular distance between the incentre and any one of the side of a triangle is called
inradius denoted by "r".
¤ Since "r" is inradius, ∆ is area of the triangle and s is semi perimeter, we have
¤ For a ∆ ABC have one incircle and three excircles therefore r1 is exradii opposite to vertex A, r2 is exradii opposite to vertex B, r3 is exradii opposite to vertex C
