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" If one of two parallel lines is perpendicular to a plane, the other will also be perpendicular to the same plane. "
Elements of Geometry and Trigonometry: With Notes - Page 126
by Adrien Marie Legendre - 1830 - 316 pages
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Elements of Analytic Geometry

Joseph Johnston Hardy - Geometry, Analytic - 1897 - 398 pages
...from the point to the plane. 35. Two straight lines perpendicular to the same plane are parallel. 36. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. 37. If two straight lines are parallel to a third straight line...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...COR.— The line BC is perpendicular to the plane of the triangle APD. PROPOSITION XI. THEOREM. 386. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. Given—AB and CD parallel, and AB perpendicular to MN. To Prove—CD...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 382 pages
...plane, not more than one line can be druu'n perpendicular to that plane. PROPOSITION IX. 342. Theorem. If one of two parallel lines is perpendicular to a plane, the other is also. MI i Given 0 F II 0' Y', 0 Y _L plane MN at O, and 0' Y' meeting plane MN at O'. To prove...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...drawn in the plane through its foot.] (§ 398) .-. AB II CD. SOLID GEOMETRY. — BOOK VI. 419. Cor. I. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. Given lines AB and CD II, and A c AB _L to plane MN. To Prove CD...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...parallel and lying in the same direction, they are equal and their planes are parallel. THEOREM VIII. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to that plane. 17 THEOREM IX. All plane angles of the same diedral angle are...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...are both _L to BD. Therefore, AB and CD are parallel. §508 § 492 § 501 § 104 0. ED 520. COR. 1. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. For if through any point O of CD a line is drawn _L to MN, it is...
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Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Solid - 1900 - 160 pages
...similarly for all other -k Why? § 330, 2 § 339 I, prop. XVI, cor. 3 PROPOSITION IX. 342. Theorem. If one of two parallel lines is perpendicular to a plane, the other is also. Given 0 Y II 0' Y', 0 Y J- plane MN at 0, and 0' Y' meeting plane MN at 0'. To prove that...
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Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1903
...OX, § 339 II ^X, and similarly for all other _k. I, prop. XVI, cor. 3 PROPOSITION IX. 342. Theorem. If one of two parallel lines is perpendicular to a plane, the other is also. Given OY II O' Y', OY J- plane MN at O, and O' Y' meeting plane MN at O'. To prove that O'Y'ħMN....
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...Whence AA'VC is a parallelogram, and AC = A'C'. LINES AND PLANES IN SPACE PROPOSITION VI. THEOREM 469. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. Hyp. AB is || to CD, and AB is -l. to plane MN. To prove CD is...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...perpendicular, is at right angles to the line of the plane. ELEMENTARY GEOMETRY [CHAP. VI 407. COROLLARY II. If one of two parallel lines is perpendicular to a plane, the other is also. For, if not, at its point of intersection with the plane erect a perpendicular. This lies...
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