Chapter 3.3, Problem 2CE

To determine

To state: the segments in the given figure which are parallel also state the postulate or theorem which justifies the answer.

Answer to Problem 2CE

  $\overline{OX}\parallel \overline{IZ}$

Postulate 11

Explanation of Solution

Given:

The diagram:

Concept Used:

Postulate 11: If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Consider the given figure:

In this figure, it can be observed that the lines $\overline{OX}$ and $\overline{IZ}$ have transversal $\overline{OI}$ such that

  $\begin{array}{c}m\angle POX=m\angle POW+m\angle WOX\\ =50+30\\ =80\end{array}$

  $\begin{array}{c}m\angle OIZ=m\angle OIY+m\angle YIZ\\ =52+28\\ =80\end{array}$

That is,

  $m\angle POX=m\angle OIZ$

This implies that,

  $\angle POX\cong \angle OIZ$

That is, the corresponding angles $\angle POX$ and $\angle OIZ$ are congruent.

Thus, by the postulate 11, it can be said that the lines $\overline{OX}$ and $\overline{IZ}$ are parallel.