How to Determine a Valid Triangle

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] X Research Source}

Table of Contents

Steps

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Learn the triangle inequality theorem. According to this theorem, the sum of the lengths of two sides of a triangle is always greater than the third side. If all three additions of the lengths are correct, then you will have a valid triangle. You need to proceed to add the lengths of each pair of sides together to make sure this is a triangle. If the triangle has side lengths a, b and c respectively, then according to the triangle inequality, we have: a+b > c, a+c > b and b+c > a. ^{[2] X Research Source}

For example, a = 7, b = 10 and c = 5.

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Checks to see if the sum of the first two edges is greater than the third. In this example, we have c = 5, a + b = 7 + 10 = 17. So, 17 > 5.

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Checks to see if the sum of the next two edges is greater than the other. ^{[3] X Research Source} Now, for b = 10, let’s see if the sum of sides a and c is greater than side b . We have: 7 + 5 = 12. So 12 > 10.

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Checks to see if the sum of the last two edges is greater than the other. With a = 7, you need to add edge b and c to see if it is larger than edge a . We have: 10 + 5 = 15 and 15 > 7, so the lengths of the three sides a, b and c form a triangle.

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Check assignments. So you have calculated the sum of the lengths of each pair of sides, check again to see if the law is correct or not. If the sum of the lengths of any two sides is greater than the other side in all cases then this is exactly the length of the three sides of the triangle, you can conclude that the triangle is valid. If the law doesn’t hold for even one pair of lengths, it’s not a triangle. Since the following calculations are correct, we have a valid triangle: ^{[4] X Research Source}

a + b > c = 17 > 5
a + c > b = 12 > 10
b + c > a = 15 > 7

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Invalid triangle recognition. See the following example to practice recognizing invalid triangles: ^{[5] X Research source} assumes we have a triangle with side lengths of 5, 8 and 3 respectively. Let’s try to test with the math:

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.

Steps

Advice

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