The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.

Home Analytic Geometry Triangle Relations between Angles and Sides
See also: Congruence Transformation, Congruent and Similar Triangles, Relations between Angles in Triangles, Half Angle Relations in a Triangle, Mollweide's Formulas, Construction of a Triangle 
del.icio.us Reddit Facebook StumbleUpon MySpace Twitter Search the VIAS Library  |  Index

Relations between Angles and Sides in Triangles

The following list summarizes the most important relationships between the angles and the sides in an arbitrary triangle:
  • The sum of the angles in a plane triangle is always constant and equal to 180° (= π radiants). α + β + γ = 180°.
    Please note that the sum of the angles deviates from 180° if the triangle is not on a plane. For example, drawing a triangle on the surface of a sphere may result in a sum of the angles of 270°.
     
  • If two sides (a and b) of a triangle are of equal length then the angles α and β are equal.
     
  • The sum of the outer angles is always 360° (2π) α + β + γ = 360°.
  • The sum of the lengths of two sides is always greater than the third side, any side is greater than the absolute value of the difference of the other two sides:
    a + b > c > |a-b|
    a + c > b > |a-c|
    c + b > a > |c-b|

Home Analytic Geometry Triangle Relations between Angles and Sides

Last Update: 2011-01-11