 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...these perpendiculars are parallel and hence (§ 464) that they are equal. PROPOSITION XL THEOREM 456. A line perpendicular to one of two parallel planes is perpendicular to the other also. M, 1 " -*jg . v Given the line AB perpendicular to the plane MN, and the plane PQ parallel to the plane... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...prove MN II PQ. HINT. Apply the indirect method and (503). PROPOSITION XIV. THEOREM 515. A straight line perpendicular to one of two parallel planes is perpendicular to the other also. 320 Proof. Through AB pass any plane intersecting MN in AC and PQ in BD, respectively. AC II BD, (483)... | |
 | George C. Shutts - 1913 - 212 pages
...point on the floor which is directly under the point on the ceiling? PROPOSITION XVIII. 476. THEOREM. A line perpendicular to one of two parallel planes is perpendicular to the other. /—%vv /—^ M / i x * / Given plane M \\ plane N and line o -L M at 0. To Prove a -L N. Proof. SUG.... | |
 | Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - Mathematics - 1914 - 270 pages
...planes are equal. Through the parallel lines pass a plane intersecting the given planes. VIII THEOREM 20 A line perpendicular to one of two parallel planes is perpendicular to the other. Through the line pass two planes intersecting the given planes, and draw the lines of intersection.... | |
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...perpendicular to the other plane lies in the first plane. [Use §§ 119 and 95.] 121. COROLLARY 2. A plane perpendicular to one of two parallel planes is perpendicular to the other plane also. 122. NOTE. It follows from § 119 and § 118 that a necessary and sufficient condition... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...are II, and it is therefore a O. § 158, 3 Hence, AC = BD. § 161 QED PROPOSITION VII. THEOREM 527. A line perpendicular to one of two parallel planes is perpendicular to the other also. Let MN and PQ be parallel planes, and AB perpendicular to MAT. To prove AB J. PQ. Proof: Through AB... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...or BC or both. § 46 14. But this is impossible. § 312 SOLID GEOMETRY 318. Theorem. — A straight line perpendicular to one of two parallel planes is perpendicular to the other also. A C \ \ Hypothesis. Plane MN\\ plane PQ ; line AB ± plane PQ. Conclusion. Line AB _L plane MN. Proof.... | |
 | William Betz - Geometry - 1916 - 536 pages
...Then b' _L P. Why? 3. But b _L P. Hyp. 4. .'. b coincides with b1, Why? and a II b. 556. A straight line perpendicular to one of two parallel planes is perpendicular to the other; and conversely, two planes perpendicular to the same line are parallel. B (a) Given the line a perpendicular... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...dihedral angles w hose faces are respectively parallel are either equal or supplementary. (d) A plane perpendicular to one of two parallel planes is perpendicular to the other. PROPOSITION XIII. THEOREM 566. If a line is perpendicular to a plane, every plane passed through the... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...prove MN II PQ. HINT. Apply the indirect method and (503). PROPOSITION XIV. THEOREM 515. A straight line perpendicular to one of two parallel planes is perpendicular to the other also. Given plane MN II plane PQ, and AB _L plane MN. To prove AB _L plane PQ. Proof. Through AB pass any... | |
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A straight line perpendicular to one of two parallel planes is perpendicular to the other also. 
