## Elementary Geometry for College Students (6th Edition)

.Given that ray AC is an angle bisector of $\angle BAD$ •$\angle 1 =\angle2$ by the definition of angle bisector. • taking the external angle of triangle ABC so $\angle ACD= \angle 1 + \angle ABC$ ( the external angle of a triangle is equal the sum of the two interior non adjacent angles ) . • by theorem $\angle ACD \gt \angle 1$ and $\angle ACD \gt \angle ABC$ • by substituting $\angle 1 by \angle 2$ since they are congruent so that $\angle ACD \gt \angle 2$. • the segment opposite to $\angle ACD is \overline{AD}$ and the segment opposite to $\angle 2 is \overline{CD}$ therefore by substitution $\overline{AD} \gt CD.$ $\square$