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If planes Q and R are parallel planes and plane Q contains line a, and plane R contains line b, what can be concluded about lines a and b in a third plane? A. lines a and b must be parallel. B. lines a and b cannot be parallel. C. lines a and b must be skew. D. lines a and b must be perpendicular.

User Melony
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1 Answer

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Final answer:

Lines a and b must be parallel in a third plane. Therefore, the correct conclusion is A. Lines a and b must be parallel.

Step-by-step explanation:

When planes Q and R are described as parallel planes, it signifies that these planes do not intersect; they extend indefinitely without ever meeting.

If plane Q contains line a, and plane R contains line b, it implies that lines a and b are coplanar with their respective planes.

When considering a third plane, lines a and b will remain parallel because parallel lines in one plane intersect parallel lines in another plane at the same angle.

Therefore, in the context of three planes, the conclusion is that lines a and b must be parallel.

This aligns with the geometric principle that parallel lines in one plane remain parallel when intersected by a third plane.

Thus, option A, stating that lines a and b must be parallel, accurately represents the geometric relationship between lines a and b in the third plane formed by planes Q and R.

User PattyOK
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