Plane and solid geometry . fN Given str. lines AB and CD J_ plane prove AB II CD. The proof is left as an exercise for the student. Hint. Suppose that AB is not |I CD, but that some other line throughB, as BE, is II CD. Use § 638. Proposition XIV. Theorem 641. If a straight line is parallel to a plane, the in-tersection of the plane ivith any plane passing throughthe given line is parallel to the given line. Ai iB. Given line AB II plane MN, and plane AD, through AB, inter-secting plane MN in line CD,To prove AB II CD, The proof is left as an exercise for the student. Hint. Suppose that
Plane and solid geometry . fN Given str. lines AB and CD J_ plane prove AB II CD. The proof is left as an exercise for the student. Hint. Suppose that AB is not |I CD, but that some other line throughB, as BE, is II CD. Use § 638. Proposition XIV. Theorem 641. If a straight line is parallel to a plane, the in-tersection of the plane ivith any plane passing throughthe given line is parallel to the given line. Ai iB. Given line AB II plane MN, and plane AD, through AB, inter-secting plane MN in line CD,To prove AB II CD, The proof is left as an exercise for the student. Hint. Suppose that AB is not II CD. Show that AB will then meetplane MN. BOOK VI 315 642. Cor. I. If a -plane intersects one of two -parallellines, it must, if suffi-ciently extended, inter-sect the other also. Hint. Pass a plane throughAB and CD and let it intersectplane MN in EF. Now if MNdoes not intersect CD^ but is II toit, then ^i^ll CD, § 641. Apply§178. 643. Cor. II. If two in- tersecting lines are each parallel to a given plane, the plane of these lines is parallel to the given plane. Hint. If plane MN^determined by AB and CD,is not II to plane BS, it willintersect it in some line, asEF. What is the relationof EF to AB and CD ?
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
