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Revision Notes: Inequalities | Mathematics Class 9 ICSE PDF Download

Important Theorems 

  • If two sides of a triangle are unequal, the greater side has the greater angle opposite to it. 
  • If two angles of a triangle are unequal, the greater angle has the greater side opposite to it. 
  • The sum of any two sides of a triangle is greater than the third side. 
  • In a triangle, the difference of the lengths of any two sides is less than the third side. 
  • Of all the straight lines that can be drawn to a straight line from a given point outside it, the perpendicular is the shortest. 
  • Perimeter of a triangle is greater than the sum of the lengths of its medians.
    Revision Notes: Inequalities | Mathematics Class 9 ICSEThus, we have, AB + BC + AC > AD + BE + CF
  • In any quadrilateral, the sum of the lengths of four sides exceeds the sum of the lengths of its diagonals. 
    Revision Notes: Inequalities | Mathematics Class 9 ICSEThus, we have (AB + BC + CD + D) A > (AC + BD)
  • If P is any point in the interior of a triangle ABC, then we have
    PA + PB < AC + BC
    Revision Notes: Inequalities | Mathematics Class 9 ICSE
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