Triangle inequality for difference of two sides — lesson. Mathematics CBSE, Class 7.

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In any triangle, the difference in the length of any two sides of a triangle is always lesser than the third side.

In here, the inequalities are as follows:

$a - b < c$

$b - c < a$ and

$c - a < b$

Example:

Consider the triangle

$ABC$ whose sides measures are

$AB = c = 3 cm, BC = a = 4 cm$ and

$AC = b =5 cm$ .

Let's check the triangle inequality for the triangle

$ABC$ ,

$a - b = 4 - 5 = -1 < 3 = c$

$b - c = 5 - 3 = 2 < 4 = a$ and

$c - a = 3 - 4 = -1 < 5 = b$

Important!

Suppose

$a, b$ and

$c$ are the sides of a triangle with

$a$ and

$b$ are known sides and

$c$ is unknown. Let's use the triangle inequality to find the third side

$c$ . As the sum of two sides

$(a+b)$ of a triangle is always greater than the third side

$(c)$ , and difference of two sides

$(a-b)$ of a triangle is always lesser than the third side

$(c)$ , the length of the third side

$(c)$ must lie between difference

$(a-b)$ and sum

$(a+b)$ .

Did you find an error?

2. Triangle inequality for difference of two sides