Question

$X$ is a point on the side BC of $△ABC$ Use the symbols $>,<or=$ to make the following statements true:

$AB+AC+BC\underline{}2AX$

Answer 1

Construction of triangle

$X$is a point on the side $BC$ of $△ABC$

We know “ The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the other two sides. ”

So,$AX<AB+BX$

$AX<AC+CX$

Adding both the equations, we get;

$AB+AC+BX+CX>2AX$

$\Rightarrow AB+AC+BC>2AX$

Hence, the true statement is $AB+AC+BC\underline{>}2AX$