∠ 3 > ∠ 1 and ∠ 4 > ∠ 2

AB + BC > AC

Segment addition theorem

The exterior angle theorem

Definition

Substitution

BC > DC and AB > AD

∠1 = ∠2

Given

Substitution

AB + BC > AD + DC

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

Algebra

BD bisects ∠ABC

∠ 3 > ∠ 2 and ∠ 4 > ∠ 1

AC = AD + DC