Question

planes s and r both intersect plane t. which statements are true based on the diagram? select three options. plane s contains points b and e. the line containing points a and b lies entirely in plane t. line v intersects lines x and y at the same point. line z intersects plane s at point c. planes r and t intersect at line y.

Explanation:

• Plane \(S\) contains points \(B\) and \(E\): Looking at the diagram, point \(E\) is not in plane \(S\). So this statement is false.
• The line containing points \(A\) and \(B\) lies entirely in plane \(T\): Points \(A\) and \(B\) are both in plane \(T\). By the property that if two points of a line are in a plane, the whole line is in the plane, this statement is true.
• Line \(v\) intersects lines \(x\) and \(y\) at the same point: Line \(v\) intersects line \(x\) at \(B\) and line \(y\) at a different point. So this statement is false.
• Line \(z\) intersects plane \(S\) at point \(C\): From the diagram, line \(z\) passes through point \(C\) which is in plane \(S\). So this statement is true.
• Planes \(R\) and \(T\) intersect at line \(y\): Planes \(R\) and \(T\) share the line \(y\). By the property that the intersection of two planes is a line, this statement is true.

Answer:

• The line containing points \(A\) and \(B\) lies entirely in plane \(T\).
• Line \(z\) intersects plane \(S\) at point \(C\).
• Planes \(R\) and \(T\) intersect at line \(y\).