 O'A', OB = O'B', AB = A'B'. I, prop. XXIV 7. .'. A ^£0 ^ A A'B'O', and Z ^fOB = Z ^'0'^'. I, prop. XII ' 2. THE RELATIVE POSITION OF A LINE AND A PLANE. PROPOSITION VI. 338. Theorem. If a line is perpendicular to each of two intersecting lines, it is...  Solid Geometry - Page 251by Wooster Woodruff Beman, David Eugene Smith - 1903Full view - About this book
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...line meets a plane, and is not perpendicular to it, it is said to be oblique to the plane. COROLLARY. If a line is perpendicular to each of two intersecting lines it is perpendicular to their plane. Theorem 7. If a line is perpendicular to each of three concurrent lines at their point... | |
 | Michigan. Department of Public Instruction - Education - 1898 - 708 pages
...all triangles having the same base and area, the isosceles has the minimum perimeter. 7. Demonstrate: If a line is perpendicular to each of two intersecting...perpendicular to every other line lying In their plane aud passing through their point of intersection. 8. The frustum of a right pyramid was 72 feet square... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...6. .\OA = O'A', OB = O'B', AB = A'B'. I, prop. XXIV 7. .'. A ABO ^ A A'B'O', and Z J05 = Z J'O'5'. I, prop. XII 2. THE RELATIVE POSITION OF A LINE AND...lying in their plane and passing through their point oj' intersection. w P Given x and z, two lines intersecting at O, and w perpendicular to x and to z;... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...rest .are evidently equal or supplemental by the theorems concerning vertical and supplemental angles. 2. THE RELATIVE POSITION OF A LINE AND A PLANE. PROPOSITION...line is perpendicular to each of two intersecting linps, it is perpendicular to every other line lying in their plane and passing through their point... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1900 - 395 pages
...XXIV 7. .'. A ABO ^ A A'&O', and Z AOB = Z A'O'B'. I, prop. XII PROP. VI.] LINES AND PLANES IN SPACE. 2. THE RELATIVE POSITION OF A LINE AND A PLANE. PROPOSITION...lying in their plane and passing through their point oj intersection. Given x and z, two lines intersecting at 0, and w perpendicular to x and to z ; also... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1900 - 400 pages
...XXV 6. .-. OA = O'A', OB = O'B', AB = A'B'. I, prop. XXIV 7. .'.AABO^AA'B'O', and Z AOB — Z A'O'B'. I, prop. XII 2. THE RELATIVE POSITION OF A LINE AND...perpendicular to every other line lying in their plane and pasxing through their point of intersection. Given P' x and «, two lines intersecting at 0, and w... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Solid - 1900 - 160 pages
...meets a plane, and is not perpendicular to it, it is said to be oblique to the plane. COROLLARIES. 1. If a line is perpendicular to each of two intersecting lines, it is perpendicular to their plane. 2. The locus of points equidistant from two given points is the plane bisecting at right... | |
 | Education - 1912 - 914 pages
...axis. SECTION II. PERPENDICULARS, AND THE MEASUREMENT OF DIHEDRAL ANGLES. Proposition 20. If a straight line is perpendicular to each of two intersecting lines it is perpendicular to the plane of those lines. Corollary I. Corollary 2. Corollary 3. Definition. Pencil of planes. Axis.... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...the plane is also oblique to the line. LINES AND PLANES PROPOSITION III. THEOREM 523 If a straight line is perpendicular to each of two intersecting lines, it is perpendicular to their plane. HYPOTHESIS. AD is perpendicular to DB and DC. CONCLUSION. AD is .L to MN, the plane of... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...the plane is also oblique to the line. LINES AND PLANES PROPOSITION III. THEOREM 523 If a straight line is perpendicular to each of two intersecting lines, it is perpendicular to their plane. HYPOTHESIS. AD^is perpendicular to DB and DC. CONCLUSION. AD is _L to MN, the plane of... | |
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