A triangle cannot be constructed from three line segments if any of them is longer than the sum of the other two.

Try this
Drag any orange dot. Notice you cannot make a triangle out of these three segments.

In the above figure, the lengths of the sides A and B add up to less than the length of C.
This violates the Triangle Inequality Theorem, and so it is not possible for the three lines segments to be made into a triangle.
In the figure above, drag both loose ends down on to the line segment C, to see why this is so.

[Thanks to Jeff Holcomb, Santa Cruz City Schools, California for the inspiration for the above applet]

- Triangle definition
- Hypotenuse
- Triangle interior angles
- Triangle exterior angles
- Triangle exterior angle theorem
- Pythagorean Theorem
- Proof of the Pythagorean Theorem
- Pythagorean triples
- Triangle circumcircle
- Triangle incircle
- Triangle medians
- Triangle altitudes
- Midsegment of a triangle
- Triangle inequality
- Side / angle relationship

- Perimeter of a triangle
- Area of a triangle
- Heron's formula
- Area of an equilateral triangle
- Area by the "side angle side" method
- Area of a triangle with fixed perimeter

- Right triangle
- Isosceles triangle
- Scalene triangle
- Equilateral triangle
- Equiangular triangle
- Obtuse triangle
- Acute triangle
- 3-4-5 triangle
- 30-60-90 triangle
- 45-45-90 triangle

- Incenter of a triangle
- Circumcenter of a triangle
- Centroid of a triangle
- Orthocenter of a triangle
- Euler line

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