## Elementary Geometry for College Students (7th Edition)

- Prove $\angle DEF\cong\angle CBA$ - Show from given that $\overline{FD}\cong\overline{AC}$ - Prove $\angle DFE\cong\angle CAB$ - Then $\triangle FED\cong\triangle ABC$ according to method AAS - Then $\overline{FE}\cong\overline{AB}$ according to CPCTC
*PLANNING: We would prove $\triangle FED\cong\triangle ABC$ according to method AAS: - Prove $\angle DEF\cong\angle CBA$ - Show from given that $\overline{FD}\cong\overline{AC}$ - Prove $\angle DFE\cong\angle CAB$ 1. $\overline{DE}\bot\overline{EF}$ and $\overline{CB}\bot\overline{AB}$. (Given) 2. $\angle DEF$ and $\angle CBA$ are right angles (the angle created from perpendicular lines are right angle) 3. $\angle DEF\cong\angle CBA$ (2 corresponding right angles are congruent) 4. $\overline{FD}\cong\overline{AC}$ (Given) 5. $\overline{AB}\parallel\overline{FE}$ (Given) 6. $\angle DFE\cong\angle CAB$ (2 alternate interior angles for 2 parallel lines are congruent) So now we have 2 angles and a non-included side of $\triangle FED$ are congruent with 2 corresponding angles and a non-included side of $\triangle ABC$. Therefore, 6. $\triangle FED\cong\triangle ABC$ (AAS) 7. $\overline{FE}\cong\overline{AB}$ (CPCTC)