which statements are true based on the diagram? check all that apply. points a, b, and d are on both planes…

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 p 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.

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 p 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.

Answer

Explanation:

Step1: Analyze each statement

  • Statement 1: Points (A), (B), and (D) are on both planes.
    • From the diagram, points (A) and (B) are on both planes, but point (D) is only on plane (R) (not on plane (P)). So this statement is false.
  • Statement 2: Point (H) is not on plane (R)
    • As shown in the diagram, point (H) is outside plane (R). So this statement is true.
  • Statement 3: Plane (P) contains point (F)
    • Point (F) is on plane (R) (not on plane (P)). So this statement is false.
  • Statement 4: Points (C), (D), and (A) are non - collinear
    • There is no straight line that can pass through points (C), (D), and (A) simultaneously. So this statement is true.
  • Statement 5: The line containing points (F) and (G) is on plane (R)
    • Points (F) and (G) are both on plane (R), so the line passing through them is on plane (R). So this statement is true.
  • Statement 6: The line containing points (F) and (H) is on plane (R)
    • Point (H) is not on plane (R), so the line passing through (F) and (H) is not on plane (R). So this statement is false.

Answer:

Point (H) is not on plane (R); Points (C), (D), and (A) are non - collinear; The line containing points (F) and (G) is on plane (R)