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

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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