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 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

Explanation:

Step 1: Analyze each statement

• Statement 1: Points \( A \), \( B \), and \( D \) are on both planes
• Point \( D \) is not on plane \( P \). So this statement is false.
• Statement 2: Point \( H \) is not on plane \( R \)
• From 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 on plane \( R \), so the line \( FG \) 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 \( FH \) is not on plane \( R \). So this statement is false.

Answer:

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