Question

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

Answer 1

1. Parallel lines are always coplanar.

The right answer is always.

This is indicated in Figure 1. You can see that the red line and the blue one lie on the same plane, therefore parallel lines are always co-planar.

2. Perpendicular lines are always coplanar.

The right answer is always.

This is illustrated in Figure 2. As you can see, the red and blue lines are perpendicular. Notice that the red line lies on the plane M and also on the plane N, and the blue line only lies on the plane N. Therefore, both lines lie on the plane N. In conclusion, perpendicular lines are always coplanar.

3. Distance around an unmarked circle can never be measured.

The right answer is never

We need to have a marked circle to measure the distance. So, the distance from the center of the circle to one point of it is the radius. Moreover, the distance between two points of the circle taking a line passing through the center is the diameter of the circle.

Answer 2

1.always
2.always
3.never