# 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).

### 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)
(d) In Equilateral triangle,   R=2r
2          :     1

#### 1 comment:

1. Triangles aren't just mathematically significant, they are also fundamental to the way we build our environments, both physical and virtual. Under the geometry section of various competitive exams whether it is engineering entrance, banking entrance examinations, Management entrance, or defence, the most critical topic within geometry is Triangle. Many questions from triangles are based on basic concepts like the understanding of sides and angles and a few elementary theorems on triangles. Orthocenter, Circumcenter, and Incenter concepts in triangle, confuse many students. Thanks for sharing compact and effective study material for such an important topic.