#1
The second inequality is related to the first.
Define,
a_1=x_2-x_1
a_2=x_3-x_2
b_1=y_2-y_1
b_2=y_3-y_2
Then,
a_1+a_2=x_3-x_1
b_1+b_2=y_3-y_1
If you substitute those values into this inequality is becomes exactly #1.
You can the result from #1 to show this one.