Chapter 7.3, Problem 57SR

To determine

To write: a two-column proof of $l\parallel m$ .

Answer to Problem 57SR

The two-column theorem $l\parallel m$ is proved.

Explanation of Solution

Given:

  $\Delta ABC\text{ and }\Delta DEF$ are triangles such that $r\parallel t\text{ and }\angle 5=\angle 6$ .

  

Calculation:

According to the question,

  $r\parallel t\text{ and }\angle 5=\angle 6$

  $\begin{array}{l}\angle 4=\angle 5\text{{Consecutive interior angles theorem}}\\ \angle 6=\angle 4\text{{Congruent suppliement theorem}}\\ \text{therefore, by consecutive interior angles theorem converse}\\ l\parallel m\end{array}$

Thus, $l\parallel m$

Hence, the two-column theorem is proved.