Triangle Inequality Property

$P$ is a point in the interior of $△ABC$ as shown in the following figure. So $AP+PC>AC$.  

$P$ is a point in the interior of $△ABC$ as shown in the following figure. So $AP+PB<AB$.

Check wether the given measurements can be the possible lengths of the triangle.

$2, 5, 7$

Check wether the given measurements can be the possible lengths of the triangle.

$3, 4, 5$

Check wether the given measurements can be the possible lengths of the triangle.

$2, 10, 15$

Check wether the given measurements can be the possible lengths of the triangle.

$5, 7, 9$

Check wether the given measurements can be the possible lengths of the triangle.

$21, 22, 43$

Check wether the given measurements can be the possible lengths of the triangle.

$3.9, 3.9, 3.9$

In $△DEF$, $DE=6 \mathrm{cm}$, $EF=8 \mathrm{cm}$ and $DF=10 \mathrm{cm}$. The smallest angle is

In $△ABC$, $\angle A=100°$, $\angle B=30°$ and $\angle C=50°$. The shortest and the longest sides of the triangle are respectively

$O$ is a point in the exterior of $△ABC$. What symbol $>, <$ or $=$ will you use to complete the statement $OA+OB$ _____ $AB$? Write two other similar statements and show that $OA+OB+OC>\frac{1}{2}\left(AB+BC+CA\right)$.

In the given figure, which of the following paths is the shortest?

$P$ is a point in the interior of $△ABC$ as shown in the following figure. State whether the given statement is true or false.

$BP+PC=BC$

Can the following be the sides of a triangle?

$45 \mathrm{mm}, 50 \mathrm{mm}, 135 \mathrm{mm}$

Can the following be the sides of a triangle?

$6 \mathrm{cm}, 8 \mathrm{cm}, 7 \mathrm{cm}$

Can the following be the sides of a triangle?

$4 \mathrm{cm}, 3 \mathrm{cm}, 5 \mathrm{cm}$

Can the following be the sides of a triangle?

$2 \mathrm{cm}, 3 \mathrm{cm}, 5 \mathrm{cm}$

Difference of any two sides of a triangle is _____ than the third side.

Sum of two sides of a triangle is greater than or equal to the third side.

Difference of any two sides of a triangle is more than the third side,