Triangles, Triangle Classification

Equilateral Triangle

If the three sides of a triangle are the same size the triangle is equilateral triangle.

Equilateral triangle properties:
1) All sides are equal.
2) Angles of every equilateral triangle are equal to 60°
3) Every altitude is also a median and a bisector.
4) Every median is also an altitude and a bisector.
5) Every bisector is also an altitude and a median.
6) If the length of a side is a the area of the equilateral triangle is ¼a²√3
7) The altitudes, medians and the bisectors of a equilateral triangle are equal to ½a√3

Isosceles Triangle

If two of the sides of a triangle are of equal size the triangle is isosceles triangle.

Properties of isosceles triangle:
The altitude to the unequal side is also the corresponding bisector and median, but is wrong for the other two altitudes.
It is also true that the median for the unequal sides is also bisector and altitude, and bisector between the two equal sides is altitude and median.

Right Triangle

A triangle with a right angle(90°) is called a right triangle.

The longest side of the right triangle(the side opposite the right angle) is called the hypotenuse(or hypothenuse) and the two short sides are legs. The altitude from either leg coincides with the other leg

Right triangle formulas(look at the figure above):

A + B = 90°

The area of a right triangle is given by the formula:
$A = \frac{1}{2}a \cdot b$

c² = a² + b²(Pythagoras' theorem)

n⋅c = a² Click for proof
m⋅c = b² Click for proof

h⋅c = a⋅b
a = c⋅sin(A) = c⋅cos(B)
b = c⋅sin(B) = c⋅cos(A)