Question

determine if each statement is always, sometimes, or never true.

1. parallel lines are
2. perpendicular lines are

coplanar.

1. distance around an unmarked circle can

be measured.

Explanation:

Step 1: Analyze "Parallel lines are coplanar"

By definition, parallel lines are lines in a plane (or the same plane) that never meet and are always equidistant. So parallel lines must lie on the same plane, meaning this is always true.

Step 2: Analyze "Perpendicular lines are coplanar"

Perpendicular lines are lines that intersect at a right angle. If two lines are perpendicular, they can be in the same plane (e.g., the x - and y - axes in a coordinate plane) or in different planes (e.g., a line on the floor and a line on a wall that meet at a right angle but are in different planes). So perpendicular lines are sometimes coplanar.

Step 3: Analyze "Distance around an unmarked circle can be measured"

The distance around a circle is its circumference, given by \(C = 2\pi r\) or \(C=\pi d\) (where \(r\) is the radius and \(d\) is the diameter). Even if a circle is unmarked, we can measure its radius (by using a ruler to measure the distance from the center to the edge, if we can identify the center) or diameter (distance across the circle through the center) and then calculate the circumference. Also, we can use methods like wrapping a string around the circle and then measuring the length of the string. So the distance around an unmarked circle can be measured, and this is always true.

Answer:

1. always
2. sometimes
3. always