Theorem that in a triangle the sum of every two sides bigger

[alex]

Does someone knows the proof of the theorem that in a triangle the sum of every two sides is bigger than the length of the third site

[MathTeacher01]

consider the triangle ABC and its height BH. The height divides the base into AH and HC.
AB is hypothenuse of triangle ABH. Therefore AB > AH
BC is hypothenuse of triangle BCH. Therefore BC > HH
AB + BC > AH + HC
Therfore: AB + BC > AC

[alex]

Thank you for the proof of the theorem. Is the proof valid when we have an acute triangle.

[leesajohnson]

Let a triangle be ABC and its height is AE

AB+BC > AE+ EC
AB+BC > AC