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Chapter 6: Q1. (page 212)

Complete the following statement with the word always, sometimes, or never.

Two lines that do not intersect are _____ parallel.

Short Answer

Expert verified

The complete statement is 鈥淭wo lines that do not intersect are sometimes parallel鈥�.

Step by step solution

01

Step 1. Apply the concept of parallel lines.

If two lines in a plane do not intersect and coplanar, they are parallel. If two lines in space and not in the same plane do not intersect, they are skew.

02

Step 2. Step description.

The lines which are coplanar and do not intersect are always parallel and non-coplanar and non-intersecting lines may not be parallel.

03

Step 3. Step description.

Since the two lines do not intersect but it is not mentioned that lines are coplanar or non-coplanar thus, the lines are sometimes parallel.

Therefore, the statement is 鈥淭wo lines that do not intersect are sometimes parallel鈥�.

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