Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. This set of side lengths satisfies the Triangle Inequality Theorem. These lengths do form a triangle. Example 2: Check whether the given side lengths form a triangle. Add any two sides and see if it is greater than the other side. This set of side lengths does not satisfy Triangle Inequality Theorem.
These lengths do not form a triangle. Subjects Near Me. Download our free learning tools apps and test prep books. Varsity Tutors does not have affiliation with universities mentioned on its website. To see examples of how to apply the triangle equality theorem, keep reading! Did this summary help you?
Yes No. Log in Social login does not work in incognito and private browsers. Please log in with your username or email to continue. No account yet? Create an account. Edit this Article. We use cookies to make wikiHow great. By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article Steps. Tips and Warnings. Related Articles. Article Summary. Learn the Triangle Inequality Theorem. This theorem simply states that the sum of two sides of a triangle must be greater than the third side.
If this is true for all three combinations, then you will have a valid triangle. You'll have to go through these combinations one by one to make sure that the triangle is possible. Check to see if the sum of the first two sides is greater than the third. Check to see if the sum of the next combination of two sides is greater than the remaining side.
Check to see if the sum of the last combination of two sides is greater than the remaining side. You need to see if the sum of side b and side c is greater than side a. Check your work. Now that you've checked the side combinations one by one, you can double check that the rule is true for all three combinations.
If the sum of any two side lengths is greater than the third in every combination, as it is for this triangle, then you've determined that the triangle is valid. If the rule is invalid for even just one combination, then the triangle is invalid. Know how to spot an invalid triangle. Just for practice, you should make sure you can spot a triangle that doesn't work as well. Since this is invalid, you can stop right here.
This triangle is not valid. Not Helpful 26 Helpful It's called an equilateral triangle, and it can work because two side lengths added together are bigger than the third side. Not Helpful 53 Helpful The resulting figure is not a triangle, because the two smaller sides must be on top of the larger side in order to connect to the larger segment's endpoints.
This figure has no area, and is a line segment, not a triangle. Not Helpful 47 Helpful Not Helpful 29 Helpful Not Helpful 39 Helpful Can the measurements 7, 24 and 26 form a triangle? If not, what kind of shape would it be? As stated above, as long as the sum of any two of those measurements is greater than the third measurement, the three "sides" will fit together to make a triangle.
0コメント