1. The problem asks to identify three true statements about the points, lines, and planes based on the given diagram description. 2. From the description: - Plane 𝒜 and plane 𝒮 intersect, and points K and N lie on their intersection, so points N and K are on both planes 𝒜 and 𝒮. - Plane 𝒷 lies below plane 𝒮, and points M, P, and Q lie on plane 𝒷. - Lines n and g lie on plane 𝒷; line n passes through M and Q, line g passes through P and Q. - Point P lies on both lines n and g on plane 𝒷, so P is their intersection. - Line d lies on plane 𝒮 and passes through points L and K; since N is on plane 𝒜 and 𝒮 but not mentioned on line d, line d does not intersect plane 𝒜 at point N. 3. Evaluating each statement: - "Points N and K are on plane 𝒜 and plane 𝒮." True. - "Points P and M are on plane 𝒷 and plane 𝒮." False, plane 𝒷 lies below 𝒮, so P and M are on 𝒷 but not on 𝒮. - "Point P is the intersection of line n and line g." True. - "Points M, P, and Q are noncollinear." False, since M, P, Q lie on lines n and g, and P is intersection of n and g, M and Q lie on n, P and Q lie on g, so M, P, Q are collinear or at least not confirmed noncollinear. - "Line d intersects plane 𝒜 at point N." False, line d passes through L and K on plane 𝒮, not N. 4. Therefore, the three true statements are: - Points N and K are on plane 𝒜 and plane 𝒮. - Point P is the intersection of line n and line g. - Points M, P, and Q are noncollinear is false, so the third true statement is none of the others; only two are true. Since the question asks to select three options, the only three true statements are: - Points N and K are on plane 𝒜 and plane 𝒮. - Point P is the intersection of line n and line g. - Points M, P, and Q are noncollinear is false, so the third true statement is not given explicitly; the only other true statement is that points M, P, and Q lie on plane 𝒷. Hence, the three true statements are: - Points N and K are on plane 𝒜 and plane 𝒮. - Points P and M are on plane 𝒷 and plane 𝒮. (False) - Point P is the intersection of line n and line g. - Points M, P, and Q are noncollinear. (False) - Line d intersects plane 𝒜 at point N. (False) Only two statements are true based on the description: the first and the third. Final answer: The true statements are: 1. Points N and K are on plane 𝒜 and plane 𝒮. 2. Point P is the intersection of line n and line g. Since only two statements are true, the user should select these two.