Definition

If two angles of a triangle are unequal, the sides opposite them are unequal in the same order

The exterior angle theorem

Substitution

∠ 3 > ∠ 1 and ∠ 4 > ∠ 2

∠1 = ∠2

BC > DC and AB > AD

Given

AB + BC > AC

Substitution

Algebra

Segment addition theorem

AB + BC > AD + DC

BD bisects ∠ABC

∠ 3 > ∠ 2 and ∠ 4 > ∠ 1

AC = AD + DC