Chapter 4, Problem 13CUR

To determine

To Find: which two lines are parallel to each other in the given figure if $\angle 1\cong \angle 4$ .

Answer to Problem 13CUR

No lines.

Explanation of Solution

Given

  

And $\angle 1\cong \angle 4$ .

Calculation:

Using theorem which states-

If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

Also. If corresponding alternate angles are equal then lines are parallel.

Here, if $\angle 1\cong \angle 9,\angle 3\cong \angle 11,\angle 2\cong \angle 4$ and $\angle 10\cong \angle 12$ , then, lines would have been parallel but $\angle 1\cong \angle 4$ are not corresponding angles therefore no two lines are parallel .

Therefore, answer is no lines.