SSS Criterion in Triangles: what is it and how do you use it? 

In geometry, there are a few different ways to determine if three given sides can form a triangle. One such way is called the SSS criterion, which stands for Side-Side-Side. In this blog post, we'll explore what the SSS criterion is and how you can use it to test whether three given sides can form a triangle. 

What is the SSS Criterion? 

The SSS criterion states that three given sides can form a triangle if and only if the sum of the lengths of any two sides is greater than the length of the third side. In other words, this means that all three sides of a potential triangle must satisfy the following inequality: 

a + b > c 

b + c > a 

c + a > b 

where a, b, and c represent the lengths of the three given sides. 

How do you use the SSS Criterion? 

To use the SSS criterion, simply plug in the lengths of the three given sides into the inequality above and see if all three inequalities are satisfied. If they are, then you know that you have a valid triangle on your hands! Otherwise, the three given sides cannot form a triangle. 

Here's an example to illustrate how this works in practice. Suppose we're given the following side lengths: 3, 4, and 5. We can plug these values into the inequality to get: 

3 + 4 > 5 

4 + 5 > 3 

5 + 3 > 4 

Since all three of these inequalities are satisfied, we know that we have a valid triangle. On the other hand, suppose we're given the following side lengths: 1, 1, and 3. We can plug these values into the inequality to get: 

1 + 1 > 3 

1 + 3 > 1 

3 + 1 > 1 

Since not all three of these inequalities are satisfied (in fact, only one is!), we know that we do not have a valid triangle. 

Conclusion

The SSS criterion is a quick and easy way to test whether three given side lengths can form a valid triangle. To use it, simply plug in the lengths of the three sides into the inequality above and see if all three inequalities are satisfied. If they are, then you have yourself a valid triangle! Otherwise, those three sides cannot form a triangle.

FAQ

What is the SSS method geometry?

The SSS method is a way of testing whether three given sides can form a triangle. To use this method, simply plug in the lengths of the three sides into the inequality above and see if all three inequalities are satisfied. If they are, then you have yourself a valid triangle! Otherwise, those three sides cannot form a triangle.

What is SSS theorem example?

The SSS theorem states that three given sides can form a triangle if and only if the sum of the lengths of any two sides is greater than the length of the third side. In other words, this means that all three sides of a potential triangle must satisfy the following inequality:

a + b > c

b + c > a

c + a > b

where a, b, and c represent the lengths of the three given sides.

What is the SSS congruence theorem?

The SSS congruence theorem states that if all three sides of two triangles are equal in length, then the two triangles are congruent. In other words, this theorem allows us to conclude that two triangles are congruent if we know that their three sides are all equal in length.

Is SSS similarity criterion?

No, the SSS criterion is not a similarity criterion. The SSS criterion is a way of testing whether three given sides can form a triangle. The similarity criterion states that two figures are similar if and only if they have the same shape but different size.