Chapter 3.3, Problem 9CE

To determine

To state: the segments in the figure which are parallel given that $m\angle 5+m\angle 6=m\angle 3+m\angle 4$ .

Answer to Problem 9CE

No parallel segments

Explanation of Solution

Given:

The diagram:

Consider the given figure:

It is given that

  $m\angle 5+m\angle 6=m\angle 3+m\angle 4$

Since $m\angle 5+m\angle 6=m\angle APL$ and $m\angle 3+m\angle 4=m\angle ARL$

This gives that,

  $m\angle APL=m\angle ARL$

That is,

  $\angle APL\cong \angle ARL$

It can be observed that these angles have no line in common and also no side is common to both the angles.

So, using this data no parallel segments can be identified.