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A triangle is one of the fundamental shapes in mathematics and geometry, consisting of three sides and three angles. It is crucial to determine the validity of a triangle to ensure accuracy in geometric calculations, construction, and various applications. A valid triangle abides by certain conditions and properties, which enable us to classify it correctly and perform precise calculations on its dimensions and angles. In this guide, we will explore the criteria and techniques to determine the validity of a triangle, providing you with the necessary knowledge to identify and work with triangles accurately.
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Determining whether a triangle is valid is easier than you think. All you need to do is use the triangle inequality theorem: in a triangle, the sum of the lengths of any two sides is always greater than the length of the other side. If all three additions of the side lengths match this theorem, you get a triangle. [1] XResearch Source
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- For example, a = 7, b = 10 and c = 5.
![Image titled Determine if Three Side Lengths Are a Triangle Step 2](https://www.wikihow.com/images_en/thumb/3/33/Determine-if-Three-Side-Lengths-Are-a-Triangle-Step-2.jpg/v4-728px-Determine-if-Three-Side-Lengths-Are-a-Triangle-Step-2.jpg)
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- a + b > c = 17 > 5
- a + c > b = 12 > 10
- b + c > a = 15 > 7
![Image titled Determine if Three Side Lengths Are a Triangle Step 6](https://www.wikihow.com/images_en/thumb/2/29/Determine-if-Three-Side-Lengths-Are-a-Triangle-Step-6.jpg/v4-728px-Determine-if-Three-Side-Lengths-Are-a-Triangle-Step-6.jpg)
- 5 + 8 > 3 = 13 > 3, so a valid edge.
- 5 + 3 > 8 = 8 > 8. This is not true so you can stop and conclude: this triangle is not valid.
Advice
- These are all basic additions, so as long as you get them right the process is simple.
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 31 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 10,052 times.
Determining whether a triangle is valid is easier than you think. All you need to do is use the triangle inequality theorem: in a triangle, the sum of the lengths of any two sides is always greater than the length of the other side. If all three additions of the side lengths match this theorem, you get a triangle. [1] XResearch Source
In conclusion, the determination of a valid triangle relies on three essential conditions: the sum of any two sides of the triangle must be greater than the length of the third side, each side length should be a positive number, and the difference between the lengths of any two sides must be smaller than the third side. By examining these criteria, one can confidently determine if a given set of side lengths can form a valid triangle. It is important to apply these principles in geometric and real-life scenarios to ensure the validity of triangles and maintain accurate calculations and measurements. Additionally, understanding the validity of triangles can aid in solving various mathematical and practical problems that involve triangles, such as in architecture, engineering, and geometry. Consequently, recognizing and applying the rules for determining a valid triangle is an essential skill for those working in various fields or simply seeking to expand their knowledge in mathematics.
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