Question
Planes S and R both intersect plane T .
Horizontal plane T intersects vertical planes S and R. Planes T and S intersect at line x. Planes T and R intersect and line y. Horizontal line v intersects line x at point B and line y at point A. Line z intersects the lower half of plane S at point C. Point D is on line z but not on a plane.
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.
Horizontal plane T intersects vertical planes S and R. Planes T and S intersect at line x. Planes T and R intersect and line y. Horizontal line v intersects line x at point B and line y at point A. Line z intersects the lower half of plane S at point C. Point D is on line z but not on a plane.
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.
Answers
GPT-4o mini
Based on the provided information, we can evaluate the statements:
1. **Plane S contains points B and E.**
- This cannot be determined from the information given, as there is no mention of point E or its relationship to plane S.
2. **The line containing points A and B lies entirely in plane T.**
- This statement is true. Since lines x and y (where A and B are points) are formed by the intersection of plane T with planes S and R, respectively, and since horizontal line v intersects both lines x and y, it follows that line AB lies in plane T.
3. **Line v intersects lines x and y at the same point.**
- This statement is false. Line v intersects line x at point B and line y at point A, so they are not the same point.
4. **Line z intersects plane S at point C.**
- This statement is true. It is stated that line z intersects the lower half of plane S at point C.
5. **Planes R and T intersect at line y.**
- This statement is true, as stated in the information that planes T and R intersect at line y.
Based on the evaluations, the three true statements are:
- 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.
1. **Plane S contains points B and E.**
- This cannot be determined from the information given, as there is no mention of point E or its relationship to plane S.
2. **The line containing points A and B lies entirely in plane T.**
- This statement is true. Since lines x and y (where A and B are points) are formed by the intersection of plane T with planes S and R, respectively, and since horizontal line v intersects both lines x and y, it follows that line AB lies in plane T.
3. **Line v intersects lines x and y at the same point.**
- This statement is false. Line v intersects line x at point B and line y at point A, so they are not the same point.
4. **Line z intersects plane S at point C.**
- This statement is true. It is stated that line z intersects the lower half of plane S at point C.
5. **Planes R and T intersect at line y.**
- This statement is true, as stated in the information that planes T and R intersect at line y.
Based on the evaluations, the three true statements are:
- 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.