Question

identify five segments skew to $overline{bc}$ using the figure shown. assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively.
a) $overline{ae}$, $overline{dh}$, $overline{hf}$, $overline{ef}$, and $overline{dc}$
b) $overline{ae}$, $overline{eh}$, $overline{hg}$, $overline{ef}$, and $overline{dh}$
c) $overline{af}$, $overline{ec}$, $overline{hg}$, $overline{bf}$, and $overline{dh}$
d) $overline{be}$, $overline{ef}$, $overline{hc}$, $overline{ad}$, and $overline{dh}$

Explanation:

Step1: Recall skew - line definition

Skew lines are non - parallel and non - intersecting lines in 3 - D space. In the context of line - segments, we check if they do not lie in the same plane as $\overline{BC}$ and do not intersect $\overline{BC}$.

Step2: Analyze option A

$\overline{DC}$ lies in the same plane as $\overline{BC}$ (the plane $ABCD$), so option A is incorrect.

Step3: Analyze option B

$\overline{AE}$, $\overline{EH}$, $\overline{HG}$, $\overline{EF}$, and $\overline{DH}$ do not lie in the same plane as $\overline{BC}$ and do not intersect $\overline{BC}$.

Step4: Analyze option C

$\overline{BF}$ lies in the same plane as $\overline{BC}$ (the plane $BCGF$), so option C is incorrect.

Step5: Analyze option D

$\overline{AD}$ lies in the same plane as $\overline{BC}$ (the plane $ABCD$), so option D is incorrect.

Answer:

B. $\overline{AE}$, $\overline{EH}$, $\overline{HG}$, $\overline{EF}$, and $\overline{DH}$