Determine which statements are true in the set of real numbers3. (Select all that apply.) (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a third plane are parallel. (d) Two planes perpendicular to a third plane are parallel. (e) Two lines parallel to a plane are parallel. (f) Two lines perpendicular to a plane are parallel. (g) Two planes parallel to a line are parallel. (h) Two planes perpendicular to a line are parallel. (i) Two planes either intersect or are parallel. (j) Two lines either intersect or are parallel. (k) A plane and a line either intersect or are parallel. Incorrect: Your answer is incorrect.

(a) True

(b) False

(c) True

(d) False

(e) False

(f) True

(g) False

(h) True

(i) True

(k) True

Step-by-step explanation:

(a) Two lines parallel to a third line are parallel

True

(b) Two lines perpendicular to a third line are parallel

Only for lines on the same plane

Therefore, false

(c) Two planes parallel to a third plane are parallel

True

(d) Two planes perpendicular to a third plane are parallel

The two planes can be at an angle to each other and so intersect

Therefore, false

(e) Two lines parallel to a plane are parallel

Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect

Therefore, false

(f) Two lines perpendicular to a plane are parallel

True

(g) Two planes parallel to a line are parallel

Where the planes are not parallel to each other, they will intersect

Therefore, false

(h) Two planes perpendicular to a line are parallel

True

(i) Two planes either intersect or are parallel

True

(k) A plane and a line either intersect or are parallel

True.