Question

1. write a flow proof for theorem 2 - 6, the converse of the same - side interior angles postulate. use the drawpad to write your flow proof. scroll down to check your answer.

Explanation:

Step1: State given information

Given that $\angle1+\angle2 = 180^{\circ}$

Step2: Recall linear - pair postulate

By the linear - pair postulate, $\angle1$ and $\angle2$ form a linear pair. So $\angle1$ and $\angle2$ are supplementary.

Step3: Use definition of parallel lines

If two lines are cut by a transversal such that a pair of same - side interior angles are supplementary, then the two lines are parallel. Since $\angle1$ and $\angle2$ are same - side interior angles and $\angle1+\angle2 = 180^{\circ}$ (supplementary), then $\ell\parallel m$.

Answer:

The flow - proof shows that if $\angle1+\angle2 = 180^{\circ}$ (where $\angle1$ and $\angle2$ are same - side interior angles formed by a transversal intersecting lines $\ell$ and $m$), then $\ell\parallel m$.