AB + BC > AC

∠ 3 > ∠ 1 and ∠ 4 > ∠ 2

Given

BC > DC and AB > AD

Substitution

Definition

Algebra

The exterior angle theorem

AB + BC > AD + DC

∠1 = ∠2

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

Substitution

Segment addition theorem

BD bisects ∠ABC

∠ 3 > ∠ 2 and ∠ 4 > ∠ 1

AC = AD + DC