Triangle lengths inequality
73029
If a,b,c are sides of a triangle, prove: $ \sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} \le \sqrt{a} + \sqrt{b} + \sqrt{c} $
37744
Prove that given $a,b,c > 0$, it is possible to construct a triangle with sides of length $a,b,c$ if and only if $pa^2+qb^2 > pqc^2$
19443
Drawing a triangle
77134
Proving a three variables inequality
77026
Proof with inequalities
33027
Maximum area of a square in a triangle
138195
An inequality for arctan$x$
94672
Why is the triangle inequality property important for metric spaces?
104272
Inequality of $\vert \text{tanh}(x)-x+\frac{x^3}{3}\vert\leq\frac{1}{8}$ for $x\in[-1/4,1/4]$
120444
Trigonometric Triangle Equality
58187
Solve the sequences inequality
114297
Extremizing sum and difference of lengths using triangle inequality
88605
Proof of the Reverse Triangle Inequality
21745
Proof of Heron's Formula for the area of a triangle
39015
Prove the triangle inequality on the sphere $S^2$ in $\mathbb{R}^3$.
23119
An application of Jensen's Inequality
67851
Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?