Chapter 3.3, Problem 1CE

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 1CE

  $\overline{KC}\parallel \overline{DE}$

Theorem 3-6

Explanation of Solution

Given:

The diagram:

Concept Used:

Theorem 3-6: If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

Consider the given figure:

In this figure, it can be observed that:

  $\begin{array}{c}m\angle EDK+m\angle DKC=62+118\\ =180\end{array}$

That is, the same-side interior angles $\angle EDK$ and $\angle DKC$ are supplementary.

Thus, by the theorem 3-6, it can be said that the lines $\overline{KC}$ and $\overline{DE}$ are parallel.