Question

ndations of euclidean geometry. planes s and r both intersect plane t. 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, planes $R$ and $T$ intersect along line $y$, so the statement "Planes $R$ and $T$ intersect at line $y$" is True.

Step2: Analyze line - plane containment

Points $A$ and $B$ are on the intersection of planes $S$, $R$ and $T$. The line containing $A$ and $B$ lies in plane $T$ as both points are in plane $T$, so "The line containing points $A$ and $B$ lies entirely in plane $T$" is True.

Step3: Analyze line - line intersection

Line $v$ intersects line $x$ at point $B$ and line $y$ at point $A$, so "Line $v$ intersects lines $x$ and $y$ at the same point" is False.

Step4: Analyze point - plane containment

Point $E$ is in plane $R$ and not in plane $S$, while point $B$ is in plane $S$. So "Plane $S$ contains points $B$ and $E$" is False.

Answer:

Planes $R$ and $T$ intersect at line $y$: True
The line containing points $A$ and $B$ lies entirely in plane $T$: True
Line $v$ intersects lines $x$ and $y$ at the same point: False
Plane $S$ contains points $B$ and $E$: False