Question

Please help me finish!!Given the following information determine which lines if any are parallel. State the converse that justifies your answer.

Answer 1

From the diagram and the information provided, we have thye following;

$\begin{gathered} \angle7+\angle19=180 \\ l\text{ and n} \\ Same\text{ side interior angles} \end{gathered}$

$\begin{gathered} \angle6\cong\angle17 \\ l\text{ and n} \\ \text{Vertically opposite angles} \end{gathered}$

$\begin{gathered} \angle9\cong\angle24 \\ m\text{ and n} \\ \text{Vertically opposite angles} \end{gathered}$

$\begin{gathered} \angle2\cong\angle21 \\ l\text{ and n } \\ \text{Vertically opposite angles} \end{gathered}$

$\begin{gathered} \angle3+\angle7=180 \\ j\text{ and k} \\ \text{ Linear pair} \end{gathered}$

$\begin{gathered} \angle6\cong\angle11 \\ j\text{ and k} \\ \text{Vertical angles} \end{gathered}$

$\begin{gathered} \angle1\cong\angle3 \\ j\text{ and k} \\ \text{Corresponding angles} \end{gathered}$

$\begin{gathered} \angle12\cong\angle15 \\ l\text{ and m} \\ \text{Vertical angles} \end{gathered}$

$\begin{gathered} \angle13+\angle16=180 \\ j\text{ and k} \\ \text{Same side exterior angles} \end{gathered}$

$\begin{gathered} \angle15\cong\angle18 \\ j\text{ and k} \\ \text{Opposite angles} \end{gathered}$