Question

Planes A and B both intersect plane S.

Vertical plane S intersects horizontal plane A and horizontal plane B. Plane S and plane A intersect at line f. Line f contains points N and K. Plane S and plane B intersect at line g. Line g contains points P and Q. Line d intersects plane A at point L.

Which statements are true based on the diagram? Select three options.

Points N and K are on plane A and plane S.
Points P and M are on plane B and plane S.
Point P is the intersection of line n and line g.
Points M, P, and Q are noncollinear.
Line d intersects plane A at point N.

Answer 1

Selected true statements:
- Points N and K are on plane A and plane S.
- Points P and M are on plane B and plane S.
- Point P is the intersection of line n and line g.

Brief reasons:
- N and K lie on line f = S ∩ A, so they lie on both plane S and plane A.
- P (and M, as shown) lie on line g = S ∩ B, so they lie on both plane S and plane B.
- P is the common point of line n and line g, so it is their intersection.

The other two are false: M, P, Q are collinear (they lie on g), and d meets plane A at L (not N).