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

Using the direct proof: 1.Given $\overline{AB}=\overline{DE}$ $\overline{AB\parallel} \overline{DE}$ $\overline{AC}=\overline{DF}$ 2. $\angle BAC = \angle EDF$ if two parallel lines are cut by a transversal then the two alternate interior angles are congruent. 3. $\triangle ABC= \triangle DEF$ by SAS 4. $\angle BCA = \angle EFD$ by CPCTC 5. $\overline{BC} \parallel \overline{FE}$ If two lines are cut by a transversal so that two alternate interior angles are congruent then these lines are parallel. $\square$