Question

Consider the following geometry problems in 3-space Enter T or F depending on whether the statement is true or false.1. Two planes parallel to a third plane are parallel 2. Two lines parallel to a plane are parallel 3. Two lines orthogonal to a third line are parallel 4. Two lines parallel to a third line are parallel 5. Two planes parallel to a line are parallel 6. Two lines orthogonal to a plane are parallel 7. Two lines either intersect or are parallel 8. Two planes either intersect or are parallel 9. Two planes orthogonal to a line are parallel 10. A plane and a line either intersect or are parallel 11.Two planes orthogonal to a third plane are parallel

Answer 1

Explanation:

1) Two planes parallel to a third plane are parallel - True

2) Two lines parallel to a plane are parallel - False

3) Two lines orthogonal to a third line are parallel - False

4) Two lines parallel to a third line are parallel - True

5) Two planes parallel to a line are parallel - False

6) Two lines orthogonal to a plane are parallel - True

7) Two lines either intersect or are parallel - False

8) Two planes either intersect or are parallel - True

9) Two planes orthogonal to a line are parallel - True

10) A plane and a line either intersect or are parallel - True

11) Two planes orthogonal to a third plane are parallel - False