exterior angles of triangle

The exterior angleMathworldPlanetmath of an angle of triangle is greater than both other angles of the triangle.

Proof.  Let us study in an arbitrary triangle ABC for example the exterior angle ACD where D is point on the lengthening of the side BC nearer to C than to B.  Let E be the midpointMathworldPlanetmathPlanetmathPlanetmath of AC.  Let BE be the median of the triangle.  We find on its lengthening the point F such that  EF=EB.  Then the triangles ABE and CEF are congruent (SAS).  Consequently, we have  ECF=BAE  and therefore  ACD>BAC.   Analogically one shows that  ACD>ABC.  


  • 1 Karl Ariva: Lobatsevski geomeetria.  Kirjastus “Valgus”, Tallinn (1992).
Title exterior angles of triangle
Canonical name ExteriorAnglesOfTriangle
Date of creation 2013-05-05 8:44:43
Last modified on 2013-05-05 8:44:43
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 2
Author pahio (2872)
Entry type Theorem
Classification msc 51M05