2019 · Q89
Consider the following inequalities in respect of any triangle ABC:
- 1AC - AB < BC
- 2BC - AC < AB
- 3AB - BC < AC
Which of the above are correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 and 2 only
- B2 and 3 only
- C1 and 3 only
- D1, 2 and 3
Explanation
Each inequality is the triangle inequality in the form |difference of two sides| < third side, e.g. AC < AB+BC gives AC−AB < BC. All three hold for every triangle.