We need to enforce either c being nonnegative or write |cu|=|c||u|.

Also, why is this called the pentagon inequality when the diagram looks like a triangle?

Good catch. (On both accounts!)

I think the statement of the Pentagon Inequality is wrong. Instead, it should be as stated in this link here.

Ha! Excellent. There are actually lots of ways to generalize the triangle inequality to other polygons.

We need to enforce either c being nonnegative or write |cu|=|c||u|.

Also, why is this called the pentagon inequality when the diagram looks like a triangle?

Good catch. (On both accounts!)

I think the statement of the Pentagon Inequality is wrong. Instead, it should be as stated in this link here.

Ha! Excellent. There are actually lots of ways to generalize the triangle inequality to other polygons.