Question

identifying objects
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

• For "Points A, B, and D are on both planes":
• Points \(A\) and \(B\) are on the intersection of the two planes (the line \(AB\)), but point \(D\) is not on both planes.
• For "Point \(H\) is not on plane \(R\)":
• Since point \(H\) is outside the plane \(R\) (as per the diagram), this statement is true.
• For "Plane \(P\) contains point \(F\)":
• Point \(F\) is on plane \(R\) and not on plane \(P\), so this statement is false.
• For "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.
• For "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 \(R\). This statement is true.
• For "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 \(R\). 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 \(R\)