Question

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

Explanation:

Step1: Analyze plane - line intersection

From the diagram, we can see that planes $R$ and $T$ intersect along a line, and that line is labeled as $y$. So the statement "Planes $R$ and $T$ intersect at line $y$" is true.

Step2: Analyze line - plane relationship

Points $A$ and $B$ are on the intersection of plane $T$ and some lines. The line passing through $A$ and $B$ lies entirely within plane $T$. So the statement "The line containing points $A$ and $B$ lies entirely in plane $T$" is true.

Step3: Analyze point - plane relationship

Point $E$ is not on plane $S$, only point $B$ is on plane $S$. So the statement "Plane $S$ contains points $B$ and $E$" is false. Also, line $v$ intersects line $x$ at point $B$ and line $y$ at point $A$, not at the same point. So the statement "Line $v$ intersects lines $x$ and $y$ at the same point" is false.

Answer:

• Planes $R$ and $T$ intersect at line $y$.
• The line containing points $A$ and $B$ lies entirely in plane $T$.
• Plane $S$ contains points $B$ and $E$ (False, for reference in analysis).
• Line $v$ intersects lines $x$ and $y$ at the same point (False, for reference in analysis).

The three correct answers are:

• Planes $R$ and $T$ intersect at line $y$.
• The line containing points $A$ and $B$ lies entirely in plane $T$.