Chapter 3.2, Problem 35PPS

To determine

To prove the Alternate Exterior Angle theorem.

Explanation of Solution

  

Here l is parallel to m.

Now we can say that angle 7 and 6, and angle 5 and 8 are congruent by vertical opposite angles theorem.

Further we can determine that angles 2 and 6, and 1 and 5 are also congruent by corresponding angles theorem.

Hence,

  $\begin{array}{l}\angle 1\cong \angle 5\cong \angle 8\\ \angle 2\cong \angle 6\cong \angle 7\end{array}$

Therefore we get,

  $\begin{array}{l}\angle 1\cong \angle 8\\ \angle 2\cong \angle 7\end{array}$

Hence proved.