Verify whether the following measures represent the sides of a right angled triangle.
$1, 2, \sqrt{3}$

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Solution

Let $△ A B C$ be a triangle where $A B = 1$ , $B C = \sqrt{3}$ and $A C = 2$ .

Now consider $A B^{2} + B C^{2}$

$A B^{2} + B C^{2} = (1)^{2} + (\sqrt{3})^{2} = 1 + 3 = 4 = (\sqrt{4})^{2} = 2^{2} = A C^{2}$

Since $A B^{2} + B C^{2} = A C^{2}$ , therefore, Pythagoras theorem is valid hence $△ A B C$ is a right angled triangle.

Hence, $1$ , $2$ and $\sqrt{3}$ represent the sides of a right angled triangle.

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