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

Definition

∠ 3 > ∠ 1 and ∠ 4 > ∠ 2

AB + BC > AC

The exterior angle theorem

Substitution

∠1 = ∠2

BC > DC and AB > AD

Segment addition theorem

Algebra

Given

AB + BC > AD + DC

Substitution

BD bisects ∠ABC

∠ 3 > ∠ 2 and ∠ 4 > ∠ 1

AC = AD + DC