 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...same plane, have the same direction ; that is, they are parallel to each other. 527. Corollary. — If one of two parallel lines is perpendicular to a plane, the other is also. 182 OBLIQUE LINES AND PLANES. 529. Theorem — If from a point without a plane, a perpendicular and... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...drawing lines through any point respectively parallel to the given lines. PROPOSITION VI. THEOREM. If one of two parallel lines is perpendicular to a plane, the other one is also perpendicular to that plane. Let PQ and RS be parallel, and let PQ be perpendicular to... | |
 | William Chauvenet - Geometry - 1877 - 396 pages
...therefore the plane MN of these lines is parallel to the plane M'N' (31). PROPOSITION XIV.— THEOREM. 33. If one of two parallel lines is perpendicular to a plane, the other ig also perpendicular to that plane. Let AB, A'B', be parallel lines, and let AB be perpendicular to... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...of the circumference drawn through these points will be the foot of the perpendicular. IV. Theorem. If one of two parallel lines is perpendicular to a plane, the other is perpendicular to the same plane. HYPOTII. AB || CD, and AB _L MN. To BE PROVED. CD_LMN. PROOF. Through... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...fourth at the same point, that fourth line and the other two are in the same plane. XI. 6. — Bight lines perpendicular to the same plane are parallel....third. XI. 21. — The plane angles of any solid angle are together less than four right angles. TABLE OF CONTENTS. PART II. SECTION VIII.— DIFFERENTIAL... | |
 | William Chauvenet, William Elwood Byerly - 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 are parallel... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...other of the intersecting lines A'B', A'C', it is parallel to M'N'. PROPOSITION XI.—THEOREM. 24. 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 AB be perpendicular to the 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 - 420 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 MN at D... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...in the same plane, and they are both J_ to BD. .-. ABis II to CD. (487) zn? (70) QED N| 510. COR. 1. If one of two parallel lines is perpendicular to a plane, the other is alno perpendicular to that plane. A c For, if AB is || to CD, and J_ to the plane MN, then a J_ to... | |
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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 
