Question

a. the plane containing the floor of the tree house is parallel to the ground
o true: the floor is level with the vertical post like the ground
o false: the plane containing the floor is not on the same plane as the ground
o true: the floor is level with the horizontal just like the ground
o false: the plane containing the floor is above the plane containing the ground
b. the lines containing the railings of the staircase, such as \\( \overleftrightarrow { a b } \\), are skew to all lines in the plane containing the ground
o true: the lines intersect the plane of the ground, so they intersect certain lines of that plane
o true: the lines do not intersect the plane of the ground, so they do not intersect any lines of that plane
o false: the lines intersect the plane of the ground, so they intersect certain lines of that plane
o false: the lines do not intersect the plane of the ground, so they do not intersect any lines of that plane
c. all the lines containing the balusters, such as \\( \overleftrightarrow { c d } \\), are perpendicular to the plane containing the floor of the tree house
o false: the lines containing the balusters never intersect the plane that contains the floor
o true: the balusters appear to be vertical, and the floor of the treehouse is horizontal. so, they are perpendicular
o false: only some of the lines containing the balusters are perpendicular to the plane containing the floor
o true: the balusters appear to be horizontal, and the floor of the treehouse is vertical. so, they are perpendicular

Explanation:

• For part a: The floor of the tree - house is a separate plane above the ground plane. So, the statement "The floor is level with the horizontal just like the ground" is false as the plane containing the floor is above the plane containing the ground.
• For part b: Skew lines are non - intersecting and non - parallel lines. But the lines containing the railings of the staircase intersect the plane of the ground. When a line intersects a plane, it intersects at least one line in that plane. So, the lines are not skew to all lines in the plane of the ground.
• For part c: If the balusters appear to be vertical and the floor of the tree - house is horizontal (a horizontal plane), then a vertical line (containing the baluster) is perpendicular to a horizontal plane.

Answer:

a. false, The plane containing the floor is above the plane containing the ground
b. false, The lines intersect the plane of the ground, so they intersect certain lines of that plane
c. true, The balusters appear to be vertical, and the floor of the treehouse is horizontal. So, they are perpendicular