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Learn the definition, formula and examples of the Triangle Inequality Theorem, which states that any side of a triangle must be shorter than the other two sides added together. See how to prove it with a simple diagram and a trigonometry index.
In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths : ‖ x + y ‖ ≤ ‖ x ‖ + ‖ y ‖ , {\displaystyle \|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,}
Learn the intuition behind the triangle inequality theorem, which states that the length of any side of a triangle is less than the sum of the other two sides. Watch a video example and read the comments from other learners who ask questions and share insights.
- 6 min
- Sal Khan
- What ways can you apply the Triangle Inqequality Theorem in real life?It can be used to determine bounds on distance. For example, if I were at school and I knew that my home is 5 miles from school and my favorite fin...
- Is it possible to figure out a triangle's full classification just using the triangle's sides, no an...Yes, By using sine, cosine, and tangent, we can figure out the angle measures.
- Could the angle be 0.00000000000001 or 179.9999999999999? Is that even possible or will it end up to...Yes this is possible for a triangle. The triangle would not be degenerate, even though it’s nearly degenerate. Any three interior angles that are p...
- im still confused can you explain it a little more pleaseBasily what he/she said.
- How do I know when to add up the shape to 180, 90, or 360 degrees?The angles of a triangle add up to 180 degrees. The angle of no shape adds up to 90 degrees. The angles of a quadrilateral add up to 360 degrees. H...
- why didn't Sal maximize the angle to 360 degrees?A triangle can't have an angle degree measure of 360 degrees. The biggest angle that a triangle can have is less than 180 degrees because the sum o...
- What if the sum of two sides are equal to the side you didn't add?That is impossible. In order for that to happen, the triangle must turn into a straight line, which wouldn't be a triangle any more. The sum of two...
Learn the rule that states the sum of any two sides of a triangle must be greater than the third side. Use the interactive applet and practice problems to test your understanding and skills.
Learn what is the triangle inequality theorem, how to prove it, and how to use it to find out if a triangle exists with given side lengths. See examples, practice questions, and FAQs on this geometry topic.
Learn the definition, examples, and applications of the triangle inequality for triangles and vectors. The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.
The triangle inequality theorem states that: a < b + c, b < a + c, c < a + b. In any triangle, the shortest distance from any vertex to the opposite side is the Perpendicular. In figure below, XP is the shortest line segment from vertex X to side YZ. Let us prove the theorem now for a triangle ABC. Triangle ABC.
