Question

$\mathrm{O}$ is the point in the exterior of $△\mathrm{ABC}$.Use the symbols$<,>\text{or}=\text{to}$make the following statements true.

$\mathrm{OA}+\mathrm{OB}\underline{}\mathrm{AB}$

Answer 1

Construction of figure;

$\mathrm{O}$ is the point in the exterior of $△\mathrm{ABC}$.

Join $\mathrm{OA},\mathrm{OB}\mathrm{and}\mathrm{OC}$.

Here, we can see $\mathrm{AOB}$ is a triangle.

We know that Triangle inequality theorem states that , Sum of the length of any two sides of a triangle is greater than the third side.

So, $\mathrm{OA}+\mathrm{OB}>\mathrm{AB}$
Hence, the given statement becomes $\mathrm{OA}+\mathrm{OB}\underline{>}\mathrm{AB}$