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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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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...perimeter of the trefoil is equal to that of the circumference of the circle, and find its area. 6. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. Can a plane always be drawn through a given point parallel to two...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...240. 232. 5. 6. 7. 8. 9. 10. U. 12. 13. 116. 110. 310 BOOK VI J, PROPOSITION X. THEOREM 636. If one. of two parallel lines is perpendicular to a plane, the other also is perpendic AC r to the plane. Given AB II CD and AB _L plane MN. To prove CD _L plane MN. ARGUMENT...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...timber with a carpenter's square continuously the line will end at its starting point. 461. THEOREM. // one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. HD -M Given GH II CD and meeting plane M in G and C respectively,...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 pages
... 422 and AB and CD are both to BD. 430 .'. AB is II to CD, by 95. QED 445. COROLLARY 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 / / •...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 488 pages
...the ends of a line is a plane perpendicular to the line at its mid-point. PROPOSITION X. THEOREM 504. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. Given AB li A'B', and A a _L plane MN. To prove A'B' _L plane MN....
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Solid Geometry

George C. Shutts - 1913 - 212 pages
...radius? Of one-half the radius? Of m times the radius? Of — times the PROPOSITION IX. 461. THEOREM. // one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. H E' Given GH \\ CD and meeting plane M in G and C respectively,...
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Solid Geometry

John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...from any point of their line of intersection, lines drawn to A and B. •/ A X / BN^ 320. Theorem. — If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. C\ A\ I D\ Hypothesis. Lines AB and CD meet plane MN at B and D,...
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Bulletin of the American Mathematical Society

American Mathematical Society - Mathematics - 1916
...and many points of intersection of the edges which are not vertices. (2) In proving (No. 555) that, if one of two parallel lines is perpendicular to a plane, the other is also, it is necessary first to prove that the second line meets the plane. (3) The notion of half-plane...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...1. AABC = AABD. .\BC = BD. Why? 2. BE is neither equal to BC nor less than-BC. Why? .'. BE>BC. 555. If one of two parallel lines is perpendicular to a plane, the other is also ; and conversely, two lines perpendicular to the same plane are parallel. I Ib' (a) Given the...
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Solid Geometry

John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...Then AB and CD are perpendicular to the same line and lie in a common plane. 90 522. THEOREM. // one of two parallel lines is perpendicular to a plane the other is also. Let AB be II CD, and -L plane MN. To prove CD -L MN. Now a -L can be drawn to MN at D (...
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