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" If the perpendicular from any vertex of a triangle to the opposite side divides that side into two segments, how does each of these segments compare in length with its adjacent side of the triangle ? Prove it. "
Proceedings of the Edinburgh Mathematical Society - Page 60
by Edinburgh Mathematical Society - 1894
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Plane and Spherical Trigonometry

Alfred Hix Welsh - Plane trigonometry - 1894 - 230 pages
...From which the sides may be determined, when the perimeter and the angles are given. THEOREM VIII. The perpendicular from any vertex of a triangle to the opposite side is equal to the product of that side by the product of the sines of the adjacent angles, divided by...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...by a line meeting BC at P. Which is the longer, AB or BP? Prove it. Also CA or PC ? Prove it. 76. If the perpendicular from any vertex of a triangle to the opposite side divides that side into two segments, how does each of these segments compare in length with its adjacent...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...a line meeting BC at P. Which' is the longer, AB or BP? Prove it. Also CA or PC ? Prove it. 76. If the perpendicular from any vertex of a triangle to the opposite side divides that side into two segments, how does each of these segments compare in length with its adjacent...
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Proceedings of the ... Annual Meeting, Volumes 17-20

Engineering - 1896
...side BC. From which the sides may be determined when their sum and the angles are given. Theorem VIII. The perpendicular from any vertex of a triangle to the opposite side is equal to that side into the product of the sine of the adjacent angles, divided by the sine of the...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 382 pages
...prove that the sum of either pair of opposite sides is less than the sum of its two diagonals. 49. If the perpendicular from any vertex of a triangle to the opposite side divides that side into two segments, how does each of these segments compare in length with its adjacent...
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Junior High School Mathematics, Volume 3

John Charles Stone - 1921 - 274 pages
...triangle with the hypotenuse twice as long as one of its legs. 4. THE ALTITUDES AND MEDIANS OF A TRIANGLE The perpendicular from any vertex of a triangle to the opposite side is called an altitude of the triangle, and the side to which it is drawn is called the corresponding...
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 460 pages
...either pair of opposite sides of a quadrilateral is less than the sum of its two diagonals. 13. If the perpendicular from any vertex of a triangle to the opposite side divides the side into two segments, how does each of these segments compare in length with the side...
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Proceedings of the Edinburgh Mathematical Society, Volume 1

Edinburgh Mathematical Society - Electronic journals - 1894 - 236 pages
...Geometrical Methods, II. 260-1 (1877). Gergonne's Annales, XIX. 37-64 (1828), or Steiner's Geia.mnv.Ut Werke, I. 193 (1881). " The perpendicular from any...furnishes a ready proof. For the diameters of the circumeircle are concurrent. The point H, where AX, BY, CZ are concurrent, is now generally called...
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