Table of Contents
Table of Contents
- Triangle Inequality Theorem
- Application of Triangle Inequality Theorem
- Summary
- What’s Next?
In the previous segment, we looked at Triangle Inequality Theorem. In this segment, we will use the Triangle inequality theorem to prove an interesting property of a triangle.
What is the Triangle inequality theorem?
The triangle inequality theorem states that ‘the sum of the lengths of any two sides of a triangle is greater than the third side’.
This means for any triangle ABC,
- AB + BC > CA
- BC + CA > AB
- AB + CA > BC
Application of triangle inequality theorem
Let us now use the triangle inequality theorem to prove that the sum of lengths of the sides of a triangle is greater than twice the length of the segment joining a vertex to the opposite side.
That is, in △ABC, to prove that AB + BC + CA > 2AD.
Figure for Proof
StatementReason: In △ABD,
AB + BD > AD
AD + BD > AB
AB + AD > BD is Triangle inequality theorem