We know in a triangle sum of any two sides is greater than the third side. Is the sum of any two angles of a triangle also greater than the third angle? Justify or contradict with an example.

Take any point $O$ in the interior of $△ABC$ as shown. State which of the following is true?

$AO+BO>AB$

Take any point $O$ in the interior of $△ABC$ as shown. State which of the following is true?

$BO+CO>BC$

Take any point $O$ in the interior of $△ABC$ as shown. State which of the following is true?

$AO+CO>AC$

Take any point $O$ in the interior of $△ABC$ as shown. State which of the following is true?

$AB+AC+BC<2(AO+BO+CO)$

The length of two sides of a triangle are $10 \mathrm{cm} \mathrm{and} 15 \mathrm{cm}$. Between what two measures should the length of the third side lie?

The length of two sides of a triangle are $10 \mathrm{cm} \mathrm{and} 8 \mathrm{cm}$. Between what two measures should the length of the third side lie?

Which of the following can be sides of a right-angled triangle?

Which of the following can be sides of a right-angled triangle?