Question

determine if each statement is always, sometimes, or never true. 1. parallel lines are coplanar. 2. perpendicular lines are coplanar. 3. distance around an unmarked circle can be measured.

Explanation:

Step1: Recall parallel - lines definition

Parallel lines in Euclidean geometry are defined as coplanar lines that do not intersect. So parallel lines are always coplanar.

Step2: Recall perpendicular - lines definition

Perpendicular lines are two lines that intersect at a right - angle. In Euclidean space, the most common and basic case is when they are coplanar. But in 3 - D space, skew lines can also be perpendicular (not intersecting but having a 90 - degree angle between their direction vectors). However, the basic and most intuitive concept of perpendicular lines is in a plane, so perpendicular lines are sometimes coplanar.

Step3: Consider circle - measurement

The distance around a circle is its circumference. For an unmarked circle, we can use a flexible measuring tape or other measuring tools to measure it. So the distance around an unmarked circle can always be measured.

Answer:

1. always
2. sometimes
3. always