Algebra

Definition

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

BC > DC and AB > AD

Substitution

Segment addition theorem

Substitution

angle 3 > angle 1 and angle 4 > angle 2

<1 = <2

Given

AB + BC > AC

AB + BC > AD + DC

The exterior angle theorem

BD bisects angle ABC

angle 3 > angle 2 and angle 4 > angle 1

AC = AD + DC