Question

Theorem 3-9 states that in a plane,two lines perpendicular to the same line are parallel.Explain why the phrase "in a plane" is needed

Answer 1

Answer on Question #54854 – Math – Geometry

Theorem 3-9 states that in a plane, two lines perpendicular to the same line are parallel. Explain why the phrase "in a plane" is needed.

Solution

If we take the rectangular solid, LK ⊥ KN, MN ⊥ KN, besides LK, KN, MN lie in the same plane (upper face KLMN), then LK || MN.

If we take LK ⊥ KN, AK ⊥ KN, besides LK, KN, AK lie in space, not on the plane, then we cannot say that LK is parallel to AK, because LK and AK intersect at point K.

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