Triangles 2

Median : Line joining the midpoint of a side of a triangle to its opposite vertex. There are 3 medians in a triangle.

 

        A median bisects the area of a triangle. AE, CD, BF are medians.

3*(AB^2+AC^2+BC^2) = 4*(CD^2+BF^2+AE^2).

Incenter: Inradius = r = height/3 (for equilateral triangle) = (AB + BC – CA )/2 (for right angled triangle) = Area/semi-perimeter (for right angled triangle).
 

Circumcenter:

 

Interior Angle Bisector:

Exterior Angle Bisector:  

 

Pythagoras Theorem: 

For a right angled triangle, Hypoteneuse^2 = Perpendiclar^2 + Base^2.

Basic proportionality Theorem or Thales Theorem:

AD/DE = AB/BC = AE/DE = AC/BC.

Midpoint Theorem:

If AE=CE and AD=BD, DE || BC.