 | Webster Wells - 1909 - 154 pages
...with any plane drawn through the line is parallel to the line.) § 362. 4. Hence plane DGHA _L BC. (If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.) § 369. 5. Then, HALBC. (All the perpendiculars to a straight... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1911 - 208 pages
...PARALLELS. 27. THEOREM. If two lines are perpendicular to the same plane, they are parallel. CONVERSELY. If one of two parallel lines is perpendicular to a plane, the other is also. Given : (1) AB and CD each -L to the plane M. To prove that AB II CD. Proof : Draw BD and... | |
 | Geometry, Plane - 1911 - 192 pages
...perimeter of the trefoil is equal to that of the circumference of the circle, and find its area. 6. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. Can a plane always be drawn through a given point parallel to two... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Solid - 1912 - 220 pages
...§240. § 232. 5. 6. 7. 8. 9. 10. U. 12. 13. § 116. § 110. 310 BOOK VI J, PROPOSITION X. THEOREM 636. If one. of two parallel lines is perpendicular to a plane, the other also is perpendic AC r to the plane. Given AB II CD and AB _L plane MN. To prove CD _L plane MN. ARGUMENT... | |
 | George Clinton Shutts - Geometry - 1912 - 392 pages
...timber with a carpenter's square continuously the line will end at its starting point. 461. THEOREM. // one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. HD -M Given GH II CD and meeting plane M in G and C respectively,... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...§ 422 and AB and CD are both ± to BD. § 430 .'. AB is II to CD, by § 95. QED 445. COROLLARY 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 / / •... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...the ends of a line is a plane perpendicular to the line at its mid-point. PROPOSITION X. THEOREM 504. If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. Given AB li A'B', and A a _L plane MN. To prove A'B' _L plane MN.... | |
 | George C. Shutts - 1913 - 212 pages
...radius? Of one-half the radius? Of m times the radius? Of — times the PROPOSITION IX. 461. THEOREM. // one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. H E' Given GH \\ CD and meeting plane M in G and C respectively,... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...parallel, and from any point of their line of intersection, lines drawn to A and B. •/ A X / BN^ 320. Theorem. — If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane. C\ A\ I D\ Hypothesis. Lines AB and CD meet plane MN at B and D,... | |
 | American Mathematical Society - Mathematics - 1916 - 580 pages
...and many points of intersection of the edges which are not vertices. (2) In proving (No. 555) that, if one of two parallel lines is perpendicular to a plane, the other is also, it is necessary first to prove that the second line meets the plane. (3) The notion of half-plane... | |
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THEOREM. If one of two parallel lines is perpendicular to a plane, the other will also be perpendicular to this plane. Let AP & ED be parallel lines, of which AP is perpendicular to the plane MN ; then will ED be also perpendicular to this plane. 
