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" If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines. "
Elements of Geometry: With Practical Applications to Mensuration - Page 170
by Benjamin Greenleaf - 1868 - 320 pages
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 148 pages
...only one plane can contain a straight line and a point without, 5. PROPOSITION II. THEOREM. 15. If a straight line is perpendicular to each of two...point of intersection it is perpendicular to the plane of those lines. Notation. Let m and n be two straight lines which determine the plane M, and p another...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...the plane at the greater distance from the foot of the perpendicular. PROPOSITION IV.—THEOREM. 10. If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane of those lines. Let AP be perpendicular to PB and PC, at their intersection P; then AP is perpendicular...
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Examinations Papers

1893 - 760 pages
...Shew that similar triangles are to one another in the duplicate ratio of corresponding medians. 4. If a straight line is perpendicular to each of two straight lines at their point of intersection, it shall also be perpendicular to the plane in which they lie. The locus of points equidistant from two...
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The Elements of Solid Geometry

William C. Bartol - Geometry, Solid - 1893 - 106 pages
...passed perpendicular to the line. PROPOSITION IV. 16. THEOREM. If a line is perpendicular to each of two lines at their point of intersection, it is perpendicular to the plane of the two lines. By our hypothesis BG and BD are perpendiculars to AB, at a common point B ; therefore...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...drawn.] ( 28.) Hence, but one perpendicular can be drawn to MN at P. 400. COR. I. A straight line perpendicular to each of two straight lines at their point of intersection is perpendicular to their plane. 401. COR. II. From a given point without a plane, one perpendicular...
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Annual Report of the Secretary of War

United States. War Department - 1896 - 1258 pages
...between the secant and its external segment. [Weight, 2.] 3. If a straight line is perpendicular to two straight lines at their point of intersection it is perpendicular to the plane of those lines. [Weight, 4.] 4. Given an equilateral triangle inscribed in a circle, and a similar...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 68 pages
...their intersection is a straight line. 472. If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines. 473. Every perpendicular that can be drawn to a straight line at a given point lies...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 370 pages
...through its foot. In the same case the plane is perpendicular to the line. PROPOSITION III. THEOREM 511. If a straight line is perpendicular to each of two...of intersection, it is perpendicular to the plane of those lines. GIVEN—the Straight line BG perpendicular to each of the two intersecting straight...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...through its foot. In the same case the plane is perpendicular to the line. PROPOSITION III. THEOREM 511. If a straight line is perpendicular to each of two...their point of intersection, it is perpendicular to Hie plane of those lines. GIVEN — the straight line BG perpendicular to each of the two intersecting...
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Examinations Papers

1898 - 868 pages
...cut two parallel straight lines in A, B, C and P, Q, R respectively, prove that AS : BC- PQ : QB. 4. If a straight line is perpendicular to each of two...intersection it is perpendicular to the plane in which they lie. Find the locus of a point equidistant from three given points. II. 1. Shew how to solve two...
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