Congruence, Inequality On sides of Triangles

Congruence, Inequality On sides of Triangles

 

Inequality Relations In a Triangle
1.  If two sides of a triangle are unequal, the longer side has greater angle opposite to it. Converse of this statement is also true.
     

2.  here \( AB > AC \Leftrightarrow \left| \!{\underline {\, {ACB} \,}} \right. > \left| \!{\underline {\, {ABC} \,}} \right. \)
    The sum of any two sides of a triangle is greater than the third side.
          
here       AB + AC > BC           (or)
             AB + BC  > AC           (or)
             BC + AC  > AB

3. The difference of any two sides of a triangle is less than the third side
       
    here    |AB-BC|< AC      (or)
              |BC-AC|< AB       (or)
              |AC-AB|< BC