| 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.... | |
| 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.... | |
| William Chauvenet - Geometry - 1887 - 331 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... | |
| William Chauvenet - Geometry - 1888 - 826 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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'... | |
| 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... | |
| |