Triangle inequality for sum of two sides — lesson. Mathematics State Board, Class 6.

UPSKILL MATH PLUS

Learn Mathematics through our AI based learning portal with the support of our Academic Experts!

In any triangle, the sum of the length of any two sides is always greater than the length of the third side.

Here \(AB = c, BC = a\) and \(CA = b\).

Thus the above inequality can be written in the notations as follows:

\(a + b > c\)

\(b + c > a\) and

\(c + a > b\).

Example:

Consider the triangle \(ABC\) with sides measures \(AB = c = 3 cm, BC = a = 4 cm\) and \(AC = b = 5 cm\).

Let's check the triangle inequality for the triangle \(ABC\),

\(a + b = 4 + 5 = 9 > 3 = c\)

\(b + c = 5 + 3 = 8 > 4 = a\) and

\(c + a = 3 + 4 = 7 > 5 = b\).

Did you find an error?

4. Triangle inequality for sum of two sides