Four points are always coplanar if they:Check all that apply.A.lie on the same line.B.lie on different planes.C.lie on different lines.D.lie in the same plane.

To determine when four points are coplanar, we need to analyze the conditions provided in the options.

A. Lie on the same line.

• If four points lie on the same line, they are considered coplanar because any line resides in a single plane.

B. Lie on different planes.

• If four points lie on different planes, they cannot be coplanar since coplanarity requires that all points lie within the same plane.

C. Lie on different lines.

• If the four points lie on different lines, it does not guarantee they are coplanar. There are configurations where points on different lines can exist in separate planes.

D. Lie in the same plane.

• If four points lie in the same plane, they are obviously coplanar.

Conclusion

The conditions that allow four points to be coplanar are:

1. They lie on the same line. (A)
2. They lie in the same plane. (D)

Therefore, the correct selections for when four points are coplanar are A and D.