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A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Plane and Solid Geometry - Σελίδα 250
των Arthur Schultze, Frank Louis Sevenoak - 1902 - 370 σελίδες
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - 1913 - 457 σελίδες
...line AB. To 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)...

Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - 1913 - 470 σελίδες
...COROLLARY 2. Two parallel planes are everywhere equidistant from each other. PROPOSITION XL THEOREM 456. A line perpendicular to one of two parallel planes is perpendicular to the other also. Given the line AB perpendicular to the plane MN, and the plane PQ parallel to the plane MN. To prove...

Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - 1913 - 470 σελίδες
...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...

Solid Geometry

George C. Shutts - 1913
...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....

Constructive Text-book of Practical Mathematics, Τόμος 3

Horace Wilmer Marsh - 1914
...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....

Solid Geometry

Sophia Foster Richardson - 1914 - 209 σελίδες
...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...

Solid Geometry

John Charles Stone, James Franklin Millis - 1916 - 174 σελίδες
...either BA 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....

Plane and Solid Geometry

William Betz - 1916 - 507 σελίδες
...II to a. 2. 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...

Solid Geometry

John H. Williams, Kenneth P. Williams - 1916 - 162 σελίδες
...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...

SOLID GEOMETRY

...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...