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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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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...would be formed by AB and a straight line parallel to PD drawn through any point of AB. THEOREM vII. If one of two parallel lines is perpendicular to a plane, the other will also le perpendicular to this plane. Let AP and ED be parallel lines, of which AP is perpendicular to the...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...would be formed by AB and a straight line parallel to PD drawn through any point of AB. THEOREM V11. If one of two parallel lines is perpendicular to a plane, the other will also be perpendicular to this plane. Let AP and ED be parallel lines, of which AP is perpendicular to the plane MN; then will...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...same plane, have the same direction ; that is, they are parallel to each other. 537. 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...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 436 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 LINE8 AND PLANE8. 529. Theorem — If from a point without a plane, a perpendicular...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 319 pages
...angles, which is impossible (Bk. I. Th. xvii. Cor. 4). Cor. If two lines are parallel, and one of them is perpendicular to a plane, the other will also be perpendicular to lite same plane. Of Planes. THEOREM VI. If two planes intersect each other at right angles, and a line...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 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 18 also perpendicular to that plane. Let AB, A'B', be parallel lines, and let AB be perpendicular to...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...the plane MN of these lines is parallel to the plane M'N' (31). PROPOSITION XIV.— THEOREM. 33. IJ 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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 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 is also perpendicular to that plane. Let AB, A'B', be parallel lines, and let n s' AB be perpendicular...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry 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...
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. 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...
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