 If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to that plane. Let AB, A'B', be parallel lines, and let n s' AB be perpendicular to the plane MN; then, A'B  Solid Geometry - Page 292by Claude Irwin Palmer - 1918 - 177 pagesFull view - About this book
 | Webster Wells - Geometry - 1899 - 180 pages
...through its foot.] . (§ 398) .-. AB II CD. [Two Js to the same str. line are ||.] (§64) 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 AB _L to plane MN. To Prove CD ± MN. Proof.... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1903 - 158 pages
...§ 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'±MN. Proof.... | |
 | 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 0'Y'±MN.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...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 -l. to plane... | |
 | 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 in a plane... | |
 | Arthur Schultze - 1901 - 392 pages
...parallelogram, and .-. A ABC = A A'B'C'. (Why?) 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 J. to plane... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...both _L to BD. Therefore, AB and CD are parallel. § 518 §508 § 492 §501 §104 QED 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 0 of CD a line is drawn _L to MN, it is il to... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...in the same plan**. But AB and CD are ± and CD are (Why?) Art. 505. Art. 121. QED 525. COR. 1. If one of two parallel lines is perpendicular to a plane, the other is perpendicular to the plane also. For, if AB and CD be ||. and AB J. plane PQ, a line drawn from C _L... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...extremities of a given straight line ? SOLID GEOMETRY — BOOK VI PROPOSITION VIII. THEOREM 534 If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. N HYPOTHESIS. AB is || to CD, and AB is _L to the plane MN at B. CONCLUSION.... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...the extremities of a given straight line ? SOLID GEOMETRY— BOOK VI PROPOSITION VIII. THEOREM 534 If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. § 117 HYPOTHESIS. AB is || to CD, and AB is -L to the plane MH at B. CONCLUSION.... | |
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