Question

given: $overline{km}paralleloverline{jh}$, $overline{km}congoverline{jh}$, $overline{jk}congoverline{kl}$
prove: $overline{hk}paralleloverline{ml}$

1. $\triangle hjkcong\triangle mkl$
2. click here to insert
3. $overline{hk}paralleloverline{ml}$

Explanation:

Step1: Recall congruent - triangle properties

Since $\triangle HJK\cong\triangle MKL$, corresponding angles are equal. So $\angle HJK=\angle MKL$.

Step2: Apply parallel - line theorem

$\angle HJK$ and $\angle MKL$ are alternate - interior angles for lines $\overline{HK}$ and $\overline{ML}$ with transversal $\overline{JL}$. If alternate - interior angles are equal, then $\overline{HK}\parallel\overline{ML}$.

Answer:

1. $\angle HJK=\angle MKL$ (Corresponding - angles of congruent triangles are equal)
2. Alternate - interior angles are equal, so the lines are parallel. (If alternate - interior angles formed by two lines and a transversal are equal, then the two lines are parallel)