The following figure is a rectangular box in which EFGH and ABCD are rectangles and BF (with a bar on top) is perpendicular to planes EFGH and ABCD.Are BD and GH parallel?
Plzz answer this question
To determine if BD and GH are parallel, we need to examine the given figure and apply some geometric principles.
In the figure described, we have a rectangular box with rectangles EFGH and ABCD, where BF (with a bar on top) is perpendicular to planes EFGH and ABCD.
To check if BD and GH are parallel, we need to analyze the relationships between the various lines and angles in the figure.
One way we can proceed is by considering the properties of rectangles. In a rectangle, opposite sides are parallel. Thus, if EFGH and ABCD are both rectangles in the figure, we can conclude that EF || HG and AB || DC.
Next, we examine BF, which is perpendicular to both planes EFGH and ABCD. Perpendicular lines form right angles, which means ∠EFG = ∠BGH and ∠ABC = ∠CBF.
Now, if we look at the quadrilateral BFGH, we can see that opposite angles are congruent: ∠BGH = ∠BFG and ∠CBF = ∠BHG.
Since ∠BGH = ∠BHG, we can conclude that BFGH is a parallelogram. In a parallelogram, opposite sides are parallel. Therefore, we can conclude that BD || GH.
So, yes, based on the given information, we can determine that BD and GH are parallel in the given figure.