Table of Contents
Table of Contents
- Triangle Inequality Theorem
- Application of Triangle Inequality Theorem
- What’s Next?
In the previous segment, we solved an example based on the Angle sum property of a triangle. 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
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Statement |
Reason |
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1 |
In △ABD,
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Triangle inequality theorem |
