Question

which statements are true based on the diagram? check all that apply. points a, b, and d are on both planes. point h is not on plane ℛ. plane ℘ contains point f. points c, d, and a are noncollinear. the line containing points f and g is on plane ℛ. the line containing points f and h is on plane ℛ.

Explanation:

Step1: Analyze point - plane relationship for A, B, D

Points A and B are on the intersection of planes $\mathcal{R}$ and $\mathcal{P}$, but point D is only on plane $\mathcal{R}$, not on both planes. So "Points A, B, and D are on both planes" is false.

Step2: Analyze position of point H

Point H is outside of plane $\mathcal{R}$, so "Point H is not on plane $\mathcal{R}$" is true.

Step3: Analyze point - plane relationship for F

Point F is on plane $\mathcal{R}$, not on plane $\mathcal{P}$, so "Plane $\mathcal{P}$ contains point F" is false.

Step4: Analyze collinearity of C, D, A

Points C, D, and A do not lie on the same straight - line, so "Points C, D, and A are non - collinear" is true.

Step5: Analyze line - plane relationship for F and G

The line containing points F and G is on plane $\mathcal{R}$ as both F and G are on plane $\mathcal{R}$, so "The line containing points F and G is on plane $\mathcal{R}$" is true.

Step6: Analyze line - plane relationship for F and H

Point H is not on plane $\mathcal{R}$, so the line containing points F and H is not on plane $\mathcal{R}$, so "The line containing points F and H is on plane $\mathcal{R}$" is false.

Answer:

• Point H is not on plane $\mathcal{R}$
• Points C, D, and A are non - collinear
• The line containing points F and G is on plane $\mathcal{R}$