Which of the following are considered skew lines?
A rectangular prism labeled ABCD on left side and EGHF on right side.
A. AC and CD
B. DH and BF
C. EG and FH
D. AE and GH
Skew lines are lines that do not intersect and are not parallel.
In the given rectangular prism, none of the pairs of lines listed intersect, but they are not skew lines because they are parallel to each other.
Therefore, none of the options listed are considered skew lines.
To determine which pairs of lines are considered skew lines, we first need to understand what skew lines are. Skew lines are two lines in space that do not intersect and are not parallel.
To visualize the given rectangular prism labeled ABCD on the left side and EGHF on the right side, we can think of it as a 3D shape where AB, BC, CD, and AD represent the edges on the left side, while EF, FG, GH, and EH represent the edges on the right side.
Now, let's analyze each option to determine if the lines mentioned in the options are skew lines:
A. AC and CD: These two lines are not skew lines since they are adjacent edges on the left side of the rectangular prism.
B. DH and BF: These two lines are not skew lines since they are adjacent edges on the right side of the rectangular prism.
C. EG and FH: These two lines are skew lines. They are not parallel and do not intersect, as EG is an edge on the right side of the rectangular prism and FH is an edge on the left side.
D. AE and GH: These two lines are not skew lines. They are not parallel and do not intersect, but they are adjacent edges on the front and back faces of the rectangular prism, respectively. Skew lines, by definition, should not be parallel, and these lines are parallel to each other.
Therefore, the correct answer is C. EG and FH are considered skew lines.
To determine which of the given lines are considered skew lines, we need to understand the properties of skew lines. Skew lines are lines that do not lie in the same plane and hence do not intersect or parallel each other.
Looking at the options:
A. AC and CD: These lines lie in the same plane and intersect each other at point C. They are not skew lines.
B. DH and BF: These lines do not lie in the same plane and do not intersect each other. They are skew lines.
C. EG and FH: These lines do not lie in the same plane and do not intersect each other. They are skew lines.
D. AE and GH: These lines lie in the same plane and intersect each other at point A. They are not skew lines.
Therefore, the skew lines among the given options are:
B. DH and BF
C. EG and FH