Thursday, 16 May 2019

Important Concepts of Triangles.

Important Concepts of Triangles.



Triangles


Centroid [Intersecting Point of medians of the triangle] : 

  • Centroid divides median of a triangle in ratio 2 : 1

→  AG/GE=2/1
AG/AE=2/3
GE/AE=1/3
  • area ∆ ABE =  1/2 area ∆ ABC
  • area ∆ AGB = 1/3 area ∆ ABC
  • area ∆ AGF = 1/6 area ∆ ABC
  • AO = OD
  • OG = 1/3 AO
  • AB² + BC² = 2BD² + 1/2 AC²
  • AB² + AC² = 2AE² + 1/2  BC²
  • CA² + CB² = 1/2 AB² + 2 FC²
  • Area ∆ FGE = 1/12 area ∆ ABC
  • 3 × (sum of side square) = 4x (sum of median square) 
  • 3 × (AB² + BC² + AC²) = 4x (AE² + BD² + CF²)
  • area ∆ ABC = 4/3 area ∆ (Formed by taking AD, BF, CE, as sides of a triangle).

  • Incenter- Intersecting Point of Internal angle Bisector.


  • Circumcenter- Intersecting Point of Perpendicular Bisector.


  • Orthocenter- Intersecting Point of Altitudes.



Important Points: -


(a) Orthocenter of right angled triangle = at right angles vertex.

(b) Circumcenter of right angled triangle = Mid-point of Hypotenuse

(c) Distance b/w incenter & circumcenter of a triangle= sq root(R^2 - 2Rr)
                                                                                (R=circumradius   r= incente)
(d) In Equilateral triangle,   R=2r
                       Circum Radius : Inradius
                                    2          :     1




No comments:

Post a Comment

Blog Archive