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:

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 \(R\)