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

- Prove $\angle 1\cong\angle 2$ - Prove $\overline{HF}\cong\overline{HK}$ - Prove $\angle FGH\cong\angle HJK$ - Then $\triangle FHG\cong\triangle HKJ$ according to method AAS - Then $\overline{FG}\cong\overline{HJ}$ according to method CPCTC
*PLANNING: We would prove $\triangle FHG\cong\triangle HKJ$ according to method AAS: - Prove $\angle 1\cong\angle 2$ - Prove $\overline{HF}\cong\overline{HK}$ - Prove $\angle FGH\cong\angle HJK$ 1. $\angle 1$ and $\angle 2$ are right angles. (Given) 2. $\angle 1\cong\angle 2$ (2 corresponding right angles are congruent) 3. H is the midpoint of $\overline{FK}$. (Given) 4. $\overline{HF}\cong\overline{HK}$ (A midpoint divides the line into 2 congruent lines) 5. $\overline{FG}\parallel\overline{HJ}$ (Given) 6. $\angle FGH\cong\angle HJK$ (2 corresponding angles for 2 parallel lines are congruent) So now we have 2 angles and a non-included side of $\triangle FHG$ are congruent with 2 corresponding angles and a non-included side of $\triangle HKJ$. Therefore, 6. $\triangle FHG\cong\triangle HKJ$ (AAS) 7. $\overline{FG}\cong\overline{HJ}$ (CPCTC)