Answer
- 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
Work Step by Step
*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)
