 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...through A, parallel to PQ ; ie, MN is parallel to PQ. PROPOSITION VII. 23. THEOREM. If one of tivo parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. B D E Let the line BA be perpendicular to the plane xy ; and let the line DC be parallel to BA ; then... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...meet however far they may be extended. PROPOSITION X. 422. Theorem. If one of two parallel straight lines is perpendicular to a plane, the other is also perpendicular to the plane. С A о D Let А В and С D be two parallel lines, meeting the plane MN in the points В and D, respectively,... | |
 | Webster Wells - 1894 - 172 pages
...plane through its foot.] (§ 398.) Whence, AB and CD are parallel. 412. COR. I. If one of two parallels is perpendicular to a plane, the other is also perpendicular to the plane. Let the Hues AB and CD be parallel, and let^iB be perpendicular to the plane MN. To prove CD perpendicular... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 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 MN. Proof.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 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' J_ MN. Proof.... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 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 line, they are parallel to each... | |
 | 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 perpendicular to MN. Dem.—Pass... | |
 | 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 they are parallel to each other. 38.... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...CD are both _L to BD. Therefore, AB and CD are parallel. §508 § 492 § 501 § 104 QBD 520. COB. 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 A -c drawn _L to MN, it is II to AB (§ 519), and CD M!_... | |
 | 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 II to AB (§ 519), and CD coincides... | |
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If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. 
