Triangle
Triangle
A 2D shape bounded by three line segments forming three internal angles.
Properties
  1. It is 2D counterpart of a pyramid or a cone.
  2. A triangle has 3 sides and 3 vertices.
  3. The sum of the measures of all 3 interior angles of a triangle is always 180°.
  4. The sum of the length of two sides of a triangle is always greater than the length of the third side.
  5. A triangle can always be split into two right triangles, irrespective of its orientation.
  6. Triangles are polygons with the least number of sides.
Area of Triangle (A)
Using Base and Height
A =
1 2
base × height
Using Three Sides (Heron's Formula)
s =
a + b + c 2
A = s ( s − a ) ( s − b ) ( s − c )
Using Two Sides and an Included Angle
A =
1 2
ab sin C
a, b: Any two sides of the triangle
C: Angle between the sides a and b (Angle opposite to the side c)
Sum of Angles of Triangle
∠A + ∠B + ∠C = 180°
Sine Rule
a sin A
=
b sin B
=
c sin C
a, b, c: Sides of the triangle
A: Angle opposite to the side a
B: Angle opposite to the side b
C: Angle opposite to the side c
Cosine Rule
a2 + b2 − 2ab cos C   =   c2
a, b, c: Sides of the triangle
C: Angle between the sides a and b (Angle opposite to the side c)
Tangent Rule
a + b a − b
  =  
tan [
1 2
(A + B)] tan [
1 2
(A − B)]
a, b: Sides of the triangle
A: Angle opposite to the side a (Angle between the sides b and c)
B: Angle opposite to the side b