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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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A Synopsis of Elementary Results in Pure and Applied ..., Volume 1, Part 1

George Shoobridge Carr - Mathematics - 1880
...in the same plane. XI. 6. — Right lines perpendicular to the same plane are parallel. XI. 8. — If one of two parallel lines is perpendicular to a plane, the other is also. XI. 20. — Any two of three plane angles containing a solid angle are greater than the third....
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A Synopsis of Elementary Results in Pure Mathematics: Containing ...

George Shoobridge Carr - Handbooks, vade-mecums, etc - 1886 - 1040 pages
...in the same plane. XI. 6. — Bight lines perpendicular to the same plane are parallel. XI. 8. — If one of two parallel lines is perpendicular to a plane, the other is also. XI. 20. — Any two of three plane angles containing a solid angle are greater than the third....
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 322 pages
...parallel and lying in the same direction, they are equal and their planes are parallel. PROPOSITION XI. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to that plane. Corollary. Two straight lines perpendicular to the same plane...
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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1888 - 322 pages
...therefore the plane MN of these lines is parallel to the plane M'N' (31). PBOPOSITIOX XIV.— TIIEOREM. 33. If one of two parallel lines is perpendicular to a plane, the oilier is also perpendicular to that plane. Let AB, A'B', be parallel lines, and let AB be perpendicular...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 393 pages
...CD lie in the same plane, and they are both J_ to BD. (487) .-. ABis || to CD. (70) QED 510. COR. 1. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to that plane. AC For, if AB is || to CD, and J_ to the plane MN, then a X to...
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The Elements of Solid Geometry

William C. Bartol - Geometry, Solid - 1893 - 112 pages
...which has been passed through A, parallel to PQ; ie, MN is parallel toPQ. PROPOSITION VII. 23. THEOREM. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. E D Let the line BA be perpendicular to the plane xy; and let the...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...parallel and lying in the same direction, they are equal and their planes are parallel. PROPOSITION XI. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to that plane. Corollary. Two straight lines perpendicular to the same plane...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...perpendicular to a plane, through a given point, by the use of two carpenter's squares. 216 Theorem 9. If one of two parallel lines is perpendicular to a plane the other is also. Given OY II OT, OY _L plane MN at 0, and O'Y' meeting plane MN at 0'. To prove that O'Y' _L...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...OC2 + OA2 - 2 . PO2 + 2 . OB2 + 2 - BC2 ; .'. PB2 = PO- + OB-> ; .'. /_ POB is a rt. ^/. Theorem 9. 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 0, and O'Y' meeting plane MN at 0'. To prove that O'Y'...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 50 pages
...its middle point. 483. Two straight lines perpendicular to the same plane are parallel. 484. Cor. 1. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. 485. Cor. 2. If two straight lines are parallel to a third straight...
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