 If a line is perpendicular to each of two lines at their point of intersection, it is perpendicular to their plane. Given FB perpendicular at B to each of two straight lines AB and BC of the plane MN. To prove FB perpendicular to the plane MN.  Solid Geometry - Page 220by Walter Burton Ford, Charles Ammerman - 1913 - 107 pagesFull view - About this book
 | 1891 - 644 pages
...<?then A + B : A~ B — P + Q : P~ Q. 2. If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to their plane. The locus of a point equidistant from three straight lines which meet in a point, but are not in the... | |
 | William C. Bartol - Geometry, Solid - 1893 - 112 pages
...straight line only one plane may be passed j)erpendicular 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 BC and BD are perpendiculars to AB, at a common point... | |
 | University of the State of New York. Examination Department - Examinations - 1894 - 412 pages
...intersecting straight lines determine the position of a plane. 3 Prove that the straight line which is perpendicular to each of two lines at their point of intersection is perpendicular to the plane of those lines. 4 A section of a right circular cone is made by a plane... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...parallel if they do not meet, however far they may be produced. PROPOSITION II. THEOREM 461. If a straight line is perpendicular to each of two lines at their point of intersection, it is perpendicular to the plane of those lines. Hyp. AB is J. to BC and BD at B. To prove AB is J. to the plane MN containing... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...parallel if they do not meet, however far they may be produced. PROPOSITION II. THEOREM 461. If a straight line is perpendicular to each of two lines at their point of intersection, it is perpendicular to the plane of those lines. Hyp. AB is -l. to BC and BD at B. To prove AB is -l. to the plane MN containing... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...parallel if they do not meet, however far they may be produced. PROPOSITION II. THEOREM 461. If a straight line is perpendicular to each of two lines at their point of intersection, it is perpendicular to the plane of those lines. Hyp. AB is -L to BC and BD at B. To prove AB is -L to the plane MN containing... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...perpendicular to every line of the plane that passes through its foot. PROPOSITION III. THEOREM 807. // a line is perpendicular to each of two lines at their...intersection, it is perpendicular to their plane. Let AB be J_ to CD and to EF at their point of intersection B. To Prove AB _L to the plane MN. Proof.... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1911 - 208 pages
...point P in their intersection, pass a plane through l, meeting M and N in /, and 12. 4. A line which is perpendicular to each of two lines at their point of intersection is perpendicular to their plane. See § 15. 5. All perpendiculars to a line at a point in it lie in... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...a point P to a plane MN (Fig. 170 a) is shorter than any other line that can be drawn from P to MN. 249. Theorem II. If a line is perpendicular to each...and through B draw any line, as BH, meeting AC at //. Prolong FB to E so that BE = FB. Join F and E to A, H, and C. Fio. 171 Then AB and BC are perpendicular... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...than any other line that can be drawn from P to MN. LINES AND PLANES IN SPACE [VI, § 249 FIG. 171 249. Theorem II. If a line is perpendicular to each...AC, and through B draw any line, as BH, meeting AC ni If. Prolong FB to E so that BE = FB. Join F and E to A, H, and C. Then AB and BC are perpendicular... | |
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