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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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A Text-book of Geometry

George Albert Wentworth - 1892 - 437 σελίδες
...equal (§ 493). Therefore all points in MS are equidistant from PQ. PROPOSITION XII. THEOREM. 495, A straight line perpendicular to one of two parallel planes is perpendicular to the other. M N Let AB be perpendicular and PQ parallel to MN. To prove that AB is perpendicular to PQ. Proof,...

A Text-book of Geometry

George Albert Wentworth - 1888 - 437 σελίδες
...equal (§ 493). Therefore all points in MN are equidistant from PQ. PROPOSITION XII. THEOREM. 495. JL straight line perpendicular to one of two parallel planes is perpendicular to the other. M Let AB be perpendicular and PQ parallel to MN. To prove that AB is perpendicular to PQ. Proof. Pass...

The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - 1893 - 126 σελίδες
...|| lines included between the || lines m, n, and hence are equal. QED PROPOSITION IX. THEOHEM. 43. A straight line perpendicular to one of two parallel planes is perpendicular to the other. Notation. Let M, N be || planes and let p be J_ to M. To prove p J_ to N. Construction. Through p in...

Elementary Geometry

William Chauvenet - 1893
...are lines in the same plane AD; therefore they are parallel. EXERCISE. PROPOSITION IX.—THEOREM. 21. A straight line perpendicular to one of two parallel planes is perpendicular to the other. Let MN and PQ be parallel planes, and let the straight line AB be perpendicular to PQ ; then it will...

Elements of Geometry

Webster Wells - 1894
...(§419.) If another plane could be drawn through A parallel to PQ, it would be perpendicular to AB. [A straight line perpendicular to one of two parallel planes is perpendicular to the other also.] (§ 421.) It would then coincide with MN. [Through a given point in a straight line, but one plane...

The Elements of Geometry

Webster Wells - 1894 - 378 σελίδες
...plane perpendicular to the same straight line are parallel. PROPOSITION XIV. THEOREM. . 421. A stmight line perpendicular to one of two parallel planes is perpendicular to the other also. Let MN and PQ be parallel planes ; and let the line AD be perpendicular to PQ. To prove AD perpendicular...

Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - 1894 - 395 σελίδες
...their vertices, they are equal and their planes are parallel. PROPOSITION XVIII. A .•.! i ..i;,i H line perpendicular to one of two parallel planes is perpendicular to the other also. PROPOSITION XIX. If tnree parallel planes are intersected by two lines, the segments of the lines are...

The Elements of Geometry

Webster Wells - 1894 - 378 σελίδες
...planes is parallel to their intersection. PROPOSITION XIV. THEOREM. 421. A straight line perpendwular to one of two parallel planes is perpendicular to the other also. Let MN and PQ be parallel planes ; and let the line AD be perpendicular to PQ. To prove AD perpendicular...

Elements of Geometry: Plane and Solid

John Macnie - 1895 - 374 σελίδες
...AB, DC, the figure AC is a parallelogram (131); whence AD = BC (136). PROPOSITION XII. THEOREM. 453. A. straight line perpendicular to one of two parallel planes is perpendicular to the other also. Given: Two parallel planes, MN, PQ, and a straight line AB perpendicular to MN ; To Prove: AB is perpendicular...

Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1895 - 320 σελίδες
...same plane T. 2. And they cannot meet, because M II N. 3. .'. they are parallel by def. COEOLLAKY. A line perpendicular to one of- two parallel planes is perpendicular to the other. Pass two planes through that line and apply th. 23 and the def. of a plane _L to a line. EXERCISES....




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