Question

Planes S and R both intersect plane T .

Which statements are true based on the diagram? Check all that apply.
[A] Plane S contains points B and E.
[B] The line containing points A and B lies entirely in plane T.
[C] Line v intersects lines x and y at the same point.
[D] Line z intersects plane S at point C.
[E] Planes R and T intersect at line y.

Answer 1

[A] Plane S contains points B and E.

False

As indicated in Figure A below, Plane S contains only point B (remarked in red). Point E (remarked in blue) lies on plane R.

[B] The line containing points A and B lies entirely in plane T.

True

As indicated in Figure B below, the line containing points A and B lies entirely in plane T. That line has been remarked in red and it is obvious that lies on plane T.

[C] Line v intersects lines x and y at the same point.

False

As indicated in Figure C below, line v intersects lines x and y, but line x in intersected at point B while line y (remarked in red) is intersected at point A (remarked in blue), and they are two different points, not the same.

[D] Line z intersects plane S at point C.

True

As indicated in Figure D below, line z that has been remarked in yellow, intersects plane S at point C that has been remarked in blue.

[E] Planes R and T intersect at line y.

True

As indicated in Figure E below, planes R and T intersect at line y. The line of intersection has been remarked in red.