Given: AD bisects ∠ CAB, AD > BD

Prove: AC > DC

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∠ 4 > ∠ 2
If two angles of a triangle are unequal, the sides opposite them are unequal in the same order
The exterior angle theorem
Substitution
AC > DC
∠ 4 > ∠ 1
AD bisects ∠ CAB, AD > BD
∠ 1 = ∠ 2
Given
Definition