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1
Apollonius Theorem If AD is the median to side BC in triangle ABC
$$2\left(AD^2+BD^2\right)=AC^2+AB^2$$
2
Area of isosceles triangle
$$\dfrac{a}{4}\sqrt{4c^2-a^2}$$ (where a,b and c are the length of the sides and b=c )
3
Altitude of an equilateral triangle
$$\ \dfrac{\sqrt{3}}{2}x$$ (where x is side)
4
Inradius of equilateral triangle
$$\ \dfrac{x}{2\sqrt{3}}$$ (where x is side)t
5
Circumradius of an equilateral triangle
$$\ \dfrac{x}{\sqrt{3}}$$ (where x is side )
6
Area of equilateral triangle
$$\ \dfrac{\sqrt{3}}{4}x^2$$ (where x is side )
7
Circumradius of any triangle
$$\dfrac{abc}{4\triangle\ }$$
8
Inradius of any triangle
$$\dfrac{\triangle\ }{s}$$
9
The line joining the midpoint of any two sides in a triangle is parallel to the third side and is half the length of the third side.
Mid-Point Theorem
10
If a line is drawn parallel to one side of a triangle such that it also intersects the other two sides, then the line always divides the two sides in the same ratio.
Basic proportionality theorem
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