Given: AD bisects ∠ CAB, AD > BD

Prove: AC > DC

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